LMFDB - Embedded newform 630.2.t.c.311.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.15
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.46653 + 0.921567i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.809270 + 1.53137i) q^{6} +(-1.89754 + 1.84373i) q^{7} +1.00000i q^{8} +(1.30143 + 2.70301i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.46653 + 0.921567i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.809270 + 1.53137i) q^{6} +(-1.89754 + 1.84373i) q^{7} +1.00000i q^{8} +(1.30143 + 2.70301i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.645696i q^{11} +(-0.0648349 + 1.73084i) q^{12} +(-0.230647 - 0.133164i) q^{13} +(-2.56518 + 0.647947i) q^{14} +(1.46653 + 0.921567i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.525609 + 0.910381i) q^{17} +(-0.224437 + 2.99159i) q^{18} +(0.938083 - 0.541602i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.48192 + 0.955176i) q^{21} +(0.322848 - 0.559189i) q^{22} -3.36670i q^{23} +(-0.921567 + 1.46653i) q^{24} +1.00000 q^{25} +(-0.133164 - 0.230647i) q^{26} +(-0.582424 + 5.16341i) q^{27} +(-2.54549 - 0.721453i) q^{28} +(2.95682 - 1.70712i) q^{29} +(0.809270 + 1.53137i) q^{30} +(2.57432 - 1.48628i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.595052 - 0.946934i) q^{33} +(-0.910381 + 0.525609i) q^{34} +(-1.89754 + 1.84373i) q^{35} +(-1.69016 + 2.47858i) q^{36} +(1.37174 + 2.37592i) q^{37} +1.08320 q^{38} +(-0.215531 - 0.407846i) q^{39} +1.00000i q^{40} +(2.16896 - 3.75676i) q^{41} +(-4.35905 - 1.41375i) q^{42} +(-5.04758 - 8.74267i) q^{43} +(0.559189 - 0.322848i) q^{44} +(1.30143 + 2.70301i) q^{45} +(1.68335 - 2.91565i) q^{46} +(-0.0268516 + 0.0465083i) q^{47} +(-1.53137 + 0.809270i) q^{48} +(0.201321 - 6.99710i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-1.60980 + 0.850719i) q^{51} -0.266328i q^{52} +(10.1657 + 5.86918i) q^{53} +(-3.08610 + 4.18043i) q^{54} -0.645696i q^{55} +(-1.84373 - 1.89754i) q^{56} +(1.87485 + 0.0702295i) q^{57} +3.41425 q^{58} +(-2.85148 - 4.93891i) q^{59} +(-0.0648349 + 1.73084i) q^{60} +(3.06877 + 1.77175i) q^{61} +2.97257 q^{62} +(-7.45314 - 2.72960i) q^{63} -1.00000 q^{64} +(-0.230647 - 0.133164i) q^{65} +(0.988797 - 0.522542i) q^{66} +(-3.61024 - 6.25312i) q^{67} -1.05122 q^{68} +(3.10264 - 4.93737i) q^{69} +(-2.56518 + 0.647947i) q^{70} +10.7565i q^{71} +(-2.70301 + 1.30143i) q^{72} +(-13.9150 - 8.03384i) q^{73} +2.74347i q^{74} +(1.46653 + 0.921567i) q^{75} +(0.938083 + 0.541602i) q^{76} +(1.19049 + 1.22523i) q^{77} +(0.0172674 - 0.460970i) q^{78} +(2.16082 - 3.74266i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-5.61257 + 7.03556i) q^{81} +(3.75676 - 2.16896i) q^{82} +(-1.83015 - 3.16992i) q^{83} +(-3.06817 - 3.40387i) q^{84} +(-0.525609 + 0.910381i) q^{85} -10.0952i q^{86} +(5.90950 + 0.221362i) q^{87} +0.645696 q^{88} +(6.12312 + 10.6056i) q^{89} +(-0.224437 + 2.99159i) q^{90} +(0.683180 - 0.172566i) q^{91} +(2.91565 - 1.68335i) q^{92} +(5.14503 + 0.192726i) q^{93} +(-0.0465083 + 0.0268516i) q^{94} +(0.938083 - 0.541602i) q^{95} +(-1.73084 - 0.0648349i) q^{96} +(-14.8734 + 8.58718i) q^{97} +(3.67290 - 5.95901i) q^{98} +(1.74533 - 0.840327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.46653	+	0.921567i	0.846702	+	0.532067i
$3$	1.46653	+	0.921567i	0.846702	+	0.532067i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.809270	+	1.53137i	0.330383	+	0.625178i
$7$	−1.89754	+	1.84373i	−0.717203	+	0.696864i
$7$	−1.89754	+	1.84373i	−0.717203	+	0.696864i
$8$			1.00000i			0.353553i
$9$	1.30143	+	2.70301i	0.433809	+	0.901005i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	0.645696i		−	0.194685i	−0.995251	−	0.0973424i	$-0.968966\pi$
$11$		−	0.645696i		−	0.194685i	0.995251	−	0.0973424i	$-0.0310342\pi$
$12$	−0.0648349	+	1.73084i	−0.0187162	+	0.499650i
$13$	−0.230647	−	0.133164i	−0.0639699	−	0.0369331i	0.467674	−	0.883901i	$-0.345092\pi$
$13$	−0.230647	−	0.133164i	−0.0639699	−	0.0369331i	−0.531644	+	0.846968i	$0.678425\pi$
$14$	−2.56518	+	0.647947i	−0.685574	+	0.173171i
$15$	1.46653	+	0.921567i	0.378657	+	0.237948i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.525609	+	0.910381i	−0.127479	+	0.220800i	−0.922699	−	0.385521i	$-0.874022\pi$
$17$	−0.525609	+	0.910381i	−0.127479	+	0.220800i	0.795220	+	0.606321i	$0.207355\pi$
$18$	−0.224437	+	2.99159i	−0.0529004	+	0.705125i
$19$	0.938083	−	0.541602i	0.215211	−	0.124252i	−0.388520	−	0.921440i	$-0.627014\pi$
$19$	0.938083	−	0.541602i	0.215211	−	0.124252i	0.603731	+	0.797188i	$0.293680\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−4.48192	+	0.955176i	−0.978036	+	0.208437i
$22$	0.322848	−	0.559189i	0.0688314	−	0.119220i
$23$		−	3.36670i		−	0.702005i	−0.936374	−	0.351003i	$-0.885841\pi$
$23$		−	3.36670i		−	0.702005i	0.936374	−	0.351003i	$-0.114159\pi$
$24$	−0.921567	+	1.46653i	−0.188114	+	0.299354i
$25$	1.00000			0.200000
$26$	−0.133164	−	0.230647i	−0.0261156	−	0.0452336i
$27$	−0.582424	+	5.16341i	−0.112088	+	0.993698i
$28$	−2.54549	−	0.721453i	−0.481052	−	0.136342i
$29$	2.95682	−	1.70712i	0.549069	−	0.317005i	−0.199678	−	0.979862i	$-0.563990\pi$
$29$	2.95682	−	1.70712i	0.549069	−	0.317005i	0.748746	+	0.662857i	$0.230656\pi$
$30$	0.809270	+	1.53137i	0.147752	+	0.279588i
$31$	2.57432	−	1.48628i	0.462361	−	0.266944i	−0.250675	−	0.968071i	$-0.580653\pi$
$31$	2.57432	−	1.48628i	0.462361	−	0.266944i	0.713037	+	0.701127i	$0.247319\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.595052	−	0.946934i	0.103585	−	0.164840i
$34$	−0.910381	+	0.525609i	−0.156129	+	0.0901412i
$35$	−1.89754	+	1.84373i	−0.320743	+	0.311647i
$36$	−1.69016	+	2.47858i	−0.281694	+	0.413096i
$37$	1.37174	+	2.37592i	0.225512	+	0.390598i	0.956473	−	0.291821i	$-0.0942612\pi$
$37$	1.37174	+	2.37592i	0.225512	+	0.390598i	−0.730961	+	0.682419i	$0.760928\pi$
$38$	1.08320			0.175719
$39$	−0.215531	−	0.407846i	−0.0345126	−	0.0653076i
$40$			1.00000i			0.158114i
$41$	2.16896	−	3.75676i	0.338735	−	0.586707i	−0.645460	−	0.763794i	$-0.723334\pi$
$41$	2.16896	−	3.75676i	0.338735	−	0.586707i	0.984195	+	0.177087i	$0.0566676\pi$
$42$	−4.35905	−	1.41375i	−0.672616	−	0.218147i
$43$	−5.04758	−	8.74267i	−0.769749	−	1.33325i	−0.937699	−	0.347449i	$-0.887048\pi$
$43$	−5.04758	−	8.74267i	−0.769749	−	1.33325i	0.167949	−	0.985796i	$-0.446286\pi$
$44$	0.559189	−	0.322848i	0.0843010	−	0.0486712i
$45$	1.30143	+	2.70301i	0.194005	+	0.402942i
$46$	1.68335	−	2.91565i	0.248196	−	0.429889i
$47$	−0.0268516	+	0.0465083i	−0.00391670	+	0.00678393i	−0.867977	−	0.496604i	$-0.834580\pi$
$47$	−0.0268516	+	0.0465083i	−0.00391670	+	0.00678393i	0.864060	+	0.503388i	$0.167913\pi$
$48$	−1.53137	+	0.809270i	−0.221034	+	0.116808i
$49$	0.201321	−	6.99710i	0.0287601	−	0.999586i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−1.60980	+	0.850719i	−0.225417	+	0.119124i
$52$		−	0.266328i		−	0.0369331i
$53$	10.1657	+	5.86918i	1.39637	+	0.806193i	0.994010	−	0.109289i	$-0.0348574\pi$
$53$	10.1657	+	5.86918i	1.39637	+	0.806193i	0.402358	+	0.915482i	$0.368191\pi$
$54$	−3.08610	+	4.18043i	−0.419965	+	0.568885i
$55$		−	0.645696i		−	0.0870657i
$56$	−1.84373	−	1.89754i	−0.246379	−	0.253570i
$57$	1.87485	+	0.0702295i	0.248330	+	0.00930212i
$58$	3.41425			0.448313
$59$	−2.85148	−	4.93891i	−0.371231	−	0.642991i	0.618524	−	0.785766i	$-0.287731\pi$
$59$	−2.85148	−	4.93891i	−0.371231	−	0.642991i	−0.989755	+	0.142775i	$0.954398\pi$
$60$	−0.0648349	+	1.73084i	−0.00837015	+	0.223450i
$61$	3.06877	+	1.77175i	0.392916	+	0.226850i	0.683423	−	0.730023i	$-0.260491\pi$
$61$	3.06877	+	1.77175i	0.392916	+	0.226850i	−0.290507	+	0.956873i	$0.593824\pi$
$62$	2.97257			0.377516
$63$	−7.45314	−	2.72960i	−0.939007	−	0.343897i
$64$	−1.00000			−0.125000
$65$	−0.230647	−	0.133164i	−0.0286082	−	0.0165170i
$66$	0.988797	−	0.522542i	0.121713	−	0.0643205i
$67$	−3.61024	−	6.25312i	−0.441061	−	0.763941i	0.556707	−	0.830709i	$-0.312065\pi$
$67$	−3.61024	−	6.25312i	−0.441061	−	0.763941i	−0.997769	+	0.0667682i	$0.978731\pi$
$68$	−1.05122			−0.127479
$69$	3.10264	−	4.93737i	0.373514	−	0.594389i
$70$	−2.56518	+	0.647947i	−0.306598	+	0.0774444i
$71$			10.7565i			1.27656i	0.769806	+	0.638278i	$0.220353\pi$
$71$			10.7565i			1.27656i	−0.769806	+	0.638278i	$0.779647\pi$
$72$	−2.70301	+	1.30143i	−0.318553	+	0.153375i
$73$	−13.9150	−	8.03384i	−1.62863	−	0.940290i	−0.984502	−	0.175372i	$-0.943887\pi$
$73$	−13.9150	−	8.03384i	−1.62863	−	0.940290i	−0.644128	−	0.764918i	$-0.722780\pi$
$74$			2.74347i			0.318922i
$75$	1.46653	+	0.921567i	0.169340	+	0.106413i
$76$	0.938083	+	0.541602i	0.107605	+	0.0621260i
$77$	1.19049	+	1.22523i	0.135669	+	0.139628i
$78$	0.0172674	−	0.460970i	0.00195514	−	0.0521946i
$79$	2.16082	−	3.74266i	0.243112	−	0.421082i	−0.718487	−	0.695540i	$-0.755165\pi$
$79$	2.16082	−	3.74266i	0.243112	−	0.421082i	0.961599	+	0.274458i	$0.0884985\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−5.61257	+	7.03556i	−0.623619	+	0.781728i
$82$	3.75676	−	2.16896i	0.414864	−	0.239522i
$83$	−1.83015	−	3.16992i	−0.200885	−	0.347944i	0.747929	−	0.663779i	$-0.231049\pi$
$83$	−1.83015	−	3.16992i	−0.200885	−	0.347944i	−0.948814	+	0.315836i	$0.897715\pi$
$84$	−3.06817	−	3.40387i	−0.334765	−	0.371393i
$85$	−0.525609	+	0.910381i	−0.0570103	+	0.0987447i
$86$		−	10.0952i		−	1.08859i
$87$	5.90950	+	0.221362i	0.633565	+	0.0237325i
$88$	0.645696			0.0688314
$89$	6.12312	+	10.6056i	0.649050	+	1.12419i	0.983350	+	0.181720i	$0.0581666\pi$
$89$	6.12312	+	10.6056i	0.649050	+	1.12419i	−0.334301	+	0.942466i	$0.608500\pi$
$90$	−0.224437	+	2.99159i	−0.0236578	+	0.315342i
$91$	0.683180	−	0.172566i	0.0716168	−	0.0180899i
$92$	2.91565	−	1.68335i	0.303977	−	0.175501i
$93$	5.14503	+	0.192726i	0.533514	+	0.0199848i
$94$	−0.0465083	+	0.0268516i	−0.00479696	+	0.00276953i
$95$	0.938083	−	0.541602i	0.0962452	−	0.0555672i
$96$	−1.73084	−	0.0648349i	−0.176653	−	0.00661719i
$97$	−14.8734	+	8.58718i	−1.51017	+	0.871896i	−0.510238	+	0.860033i	$0.670443\pi$
$97$	−14.8734	+	8.58718i	−1.51017	+	0.871896i	−0.999930	+	0.0118630i	$0.996224\pi$
$98$	3.67290	−	5.95901i	0.371019	−	0.601951i
$99$	1.74533	−	0.840327i	0.175412	−	0.0844561i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	0.448592			0.0446366			0.0223183	−	0.999751i	$-0.492895\pi$
$101$	0.448592			0.0446366			0.0223183	+	0.999751i	$0.492895\pi$
$102$	−1.81949	−	0.0681556i	−0.180156	−	0.00674841i
$103$		−	5.66944i		−	0.558627i	−0.960200	−	0.279313i	$-0.909893\pi$
$103$		−	5.66944i		−	0.558627i	0.960200	−	0.279313i	$-0.0901068\pi$
$104$	0.133164	−	0.230647i	0.0130578	−	0.0226168i
$105$	−4.48192	+	0.955176i	−0.437391	+	0.0932157i
$106$	5.86918	+	10.1657i	0.570065	+	0.987381i
$107$	3.32116	−	1.91747i	0.321069	−	0.185369i	−0.330800	−	0.943701i	$-0.607319\pi$
$107$	3.32116	−	1.91747i	0.321069	−	0.185369i	0.651869	+	0.758332i	$0.273985\pi$
$108$	−4.76285	+	2.07731i	−0.458306	+	0.199889i
$109$	7.71722	−	13.3666i	0.739175	−	1.28029i	−0.213692	−	0.976901i	$-0.568549\pi$
$109$	7.71722	−	13.3666i	0.739175	−	1.28029i	0.952867	−	0.303388i	$-0.0981178\pi$
$110$	0.322848	−	0.559189i	0.0307824	−	0.0533166i
$111$	−0.177873	+	4.74850i	−0.0168829	+	0.450708i
$112$	−0.647947	−	2.56518i	−0.0612252	−	0.242387i
$113$	2.73453	+	1.57878i	0.257243	+	0.148519i	0.623076	−	0.782161i	$-0.285883\pi$
$113$	2.73453	+	1.57878i	0.257243	+	0.148519i	−0.365833	+	0.930680i	$0.619216\pi$
$114$	1.58855	+	0.998246i	0.148782	+	0.0934943i
$115$		−	3.36670i		−	0.313946i
$116$	2.95682	+	1.70712i	0.274534	+	0.158502i
$117$	0.0597740	−	0.796745i	0.00552611	−	0.0736591i
$118$		−	5.70296i		−	0.525000i
$119$	−0.681133	−	2.69657i	−0.0624393	−	0.247194i
$120$	−0.921567	+	1.46653i	−0.0841272	+	0.133875i
$121$	10.5831			0.962098
$122$	1.77175	+	3.06877i	0.160407	+	0.277833i
$123$	6.64296	−	3.51055i	0.598975	−	0.316536i
$124$	2.57432	+	1.48628i	0.231181	+	0.133472i
$125$	1.00000			0.0894427
$126$	−5.08981	−	6.09047i	−0.453436	−	0.542582i
$127$	7.18440			0.637512			0.318756	−	0.947837i	$-0.396735\pi$
$127$	7.18440			0.637512			0.318756	+	0.947837i	$0.396735\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.654519	−	17.4731i	0.0576272	−	1.53842i
$130$	−0.133164	−	0.230647i	−0.0116793	−	0.0202291i
$131$	−0.0747982			−0.00653515			−0.00326757	−	0.999995i	$-0.501040\pi$
$131$	−0.0747982			−0.00653515			−0.00326757	+	0.999995i	$0.501040\pi$
$132$	1.11759	+	0.0418637i	0.0972741	+	0.00364376i
$133$	−0.781482	+	2.75728i	−0.0677630	+	0.239087i
$134$		−	7.22048i		−	0.623755i
$135$	−0.582424	+	5.16341i	−0.0501271	+	0.444395i
$136$	−0.910381	−	0.525609i	−0.0780645	−	0.0450706i
$137$			7.85974i			0.671503i	0.941951	+	0.335751i	$0.108990\pi$
$137$			7.85974i			0.671503i	−0.941951	+	0.335751i	$0.891010\pi$
$138$	5.15565	−	2.72457i	0.438878	−	0.231931i
$139$	−19.3599	−	11.1774i	−1.64209	−	0.948058i	−0.980091	−	0.198550i	$-0.936377\pi$
$139$	−19.3599	−	11.1774i	−1.64209	−	0.948058i	−0.661995	−	0.749509i	$-0.730290\pi$
$140$	−2.54549	−	0.721453i	−0.215133	−	0.0609739i
$141$	−0.0822392	+	0.0434603i	−0.00692579	+	0.00366002i
$142$	−5.37823	+	9.31536i	−0.451331	+	0.781728i
$143$	−0.0859835	+	0.148928i	−0.00719030	+	0.0124540i
$144$	−2.99159	−	0.224437i	−0.249299	−	0.0187031i
$145$	2.95682	−	1.70712i	0.245551	−	0.141769i
$146$	−8.03384	−	13.9150i	−0.664885	−	1.15162i
$147$	6.74354	−	10.0759i	0.556198	−	0.831050i
$148$	−1.37174	+	2.37592i	−0.112756	+	0.195299i
$149$		−	15.7141i		−	1.28735i	−0.765301	−	0.643673i	$-0.777410\pi$
$149$		−	15.7141i		−	1.28735i	0.765301	−	0.643673i	$-0.222590\pi$
$150$	0.809270	+	1.53137i	0.0660766	+	0.125036i
$151$	6.46602			0.526197			0.263099	−	0.964769i	$-0.415256\pi$
$151$	6.46602			0.526197			0.263099	+	0.964769i	$0.415256\pi$
$152$	0.541602	+	0.938083i	0.0439297	+	0.0760885i
$153$	−3.14482	−	0.235932i	−0.254243	−	0.0190740i
$154$	0.418377	+	1.65633i	0.0337138	+	0.133471i
$155$	2.57432	−	1.48628i	0.206774	−	0.119381i
$156$	0.245439	−	0.390578i	0.0196509	−	0.0312713i
$157$	−13.1731	+	7.60552i	−1.05133	+	0.606986i	−0.923022	−	0.384748i	$-0.874288\pi$
$157$	−13.1731	+	7.60552i	−1.05133	+	0.606986i	−0.128310	+	0.991734i	$0.540955\pi$
$158$	3.74266	−	2.16082i	0.297750	−	0.171906i
$159$	9.49949	+	17.9757i	0.753359	+	1.42557i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	6.20728	+	6.38845i	0.489202	+	0.503480i
$162$	−8.37841	+	3.28669i	−0.658270	+	0.258226i
$163$	−5.32485	−	9.22290i	−0.417074	−	0.722394i	0.578570	−	0.815633i	$-0.303611\pi$
$163$	−5.32485	−	9.22290i	−0.417074	−	0.722394i	−0.995644	+	0.0932394i	$0.970278\pi$
$164$	4.33793			0.338735
$165$	0.595052	−	0.946934i	0.0463248	−	0.0737187i
$166$		−	3.66030i		−	0.284095i
$167$	−9.89716	+	17.1424i	−0.765865	+	1.32652i	0.173923	+	0.984759i	$0.444356\pi$
$167$	−9.89716	+	17.1424i	−0.765865	+	1.32652i	−0.939788	+	0.341758i	$0.888978\pi$
$168$	−0.955176	−	4.48192i	−0.0736935	−	0.345788i
$169$	−6.46453	−	11.1969i	−0.497272	−	0.861300i
$170$	−0.910381	+	0.525609i	−0.0698230	+	0.0403124i
$171$	2.68481	+	1.83079i	0.205312	+	0.140004i
$172$	5.04758	−	8.74267i	0.384875	−	0.666623i
$173$	7.03552	−	12.1859i	0.534900	−	0.926475i	−0.464268	−	0.885695i	$-0.653682\pi$
$173$	7.03552	−	12.1859i	0.534900	−	0.926475i	0.999168	−	0.0407797i	$-0.0129842\pi$
$174$	5.00710	+	3.14646i	0.379587	+	0.238532i
$175$	−1.89754	+	1.84373i	−0.143441	+	0.139373i
$176$	0.559189	+	0.322848i	0.0421505	+	0.0243356i
$177$	0.369751	−	9.87090i	0.0277922	−	0.741942i
$178$			12.2462i			0.917895i
$179$	12.0062	+	6.93177i	0.897383	+	0.518105i	0.876350	−	0.481674i	$-0.159971\pi$
$179$	12.0062	+	6.93177i	0.897383	+	0.518105i	0.0210331	+	0.999779i	$0.493304\pi$
$180$	−1.69016	+	2.47858i	−0.125977	+	0.184742i
$181$			9.82773i			0.730489i	0.930912	+	0.365245i	$0.119015\pi$
$181$			9.82773i			0.730489i	−0.930912	+	0.365245i	$0.880985\pi$
$182$	0.677935	+	0.192143i	0.0502519	+	0.0142426i
$183$	2.86765	+	5.42641i	0.211983	+	0.401132i
$184$	3.36670			0.248196
$185$	1.37174	+	2.37592i	0.100852	+	0.174681i
$186$	4.35936	+	2.73942i	0.319644	+	0.200864i
$187$	0.587830	+	0.339384i	0.0429864	+	0.0248182i
$188$	−0.0537031			−0.00391670
$189$	−8.41476	−	10.8716i	−0.612083	−	0.790793i
$190$	1.08320			0.0785839
$191$	−16.5052	−	9.52928i	−1.19427	−	0.689514i	−0.235001	−	0.971995i	$-0.575509\pi$
$191$	−16.5052	−	9.52928i	−1.19427	−	0.689514i	−0.959273	+	0.282481i	$0.908843\pi$
$192$	−1.46653	−	0.921567i	−0.105838	−	0.0665084i
$193$	7.28322	+	12.6149i	0.524258	+	0.908041i	0.999601	+	0.0282405i	$0.00899044\pi$
$193$	7.28322	+	12.6149i	0.524258	+	0.908041i	−0.475344	+	0.879800i	$0.657676\pi$
$194$	−17.1744			−1.23305
$195$	−0.215531	−	0.407846i	−0.0154345	−	0.0292064i
$196$	6.16033	−	3.32420i	0.440024	−	0.237443i
$197$			18.1177i			1.29083i	0.763832	+	0.645415i	$0.223316\pi$
$197$			18.1177i			1.29083i	−0.763832	+	0.645415i	$0.776684\pi$
$198$	1.93166	+	0.144918i	0.137277	+	0.0102989i
$199$	−13.5035	−	7.79625i	−0.957237	−	0.552661i	−0.0619157	−	0.998081i	$-0.519721\pi$
$199$	−13.5035	−	7.79625i	−0.957237	−	0.552661i	−0.895322	+	0.445420i	$0.853054\pi$
$200$			1.00000i			0.0707107i
$201$	0.468140	−	12.4975i	0.0330200	−	0.881504i
$202$	0.388492	+	0.224296i	0.0273342	+	0.0157814i
$203$	−2.46322	+	8.69092i	−0.172884	+	0.609983i
$204$	−1.54164	−	0.968768i	−0.107937	−	0.0678273i
$205$	2.16896	−	3.75676i	0.151487	−	0.262383i
$206$	2.83472	−	4.90988i	0.197504	−	0.342088i
$207$	9.10023	−	4.38152i	0.632510	−	0.304536i
$208$	0.230647	−	0.133164i	0.0159925	−	0.00923327i
$209$	−0.349710	−	0.605716i	−0.0241900	−	0.0418983i
$210$	−4.35905	−	1.41375i	−0.300803	−	0.0975583i
$211$	−1.65595	+	2.86818i	−0.114000	+	0.197454i	−0.917380	−	0.398013i	$-0.869700\pi$
$211$	−1.65595	+	2.86818i	−0.114000	+	0.197454i	0.803380	+	0.595467i	$0.203033\pi$
$212$			11.7384i			0.806193i
$213$	−9.91279	+	15.7747i	−0.679213	+	1.08086i
$214$	3.83495			0.262152
$215$	−5.04758	−	8.74267i	−0.344242	−	0.596245i
$216$	−5.16341	−	0.582424i	−0.351325	−	0.0396289i
$217$	−2.14457	+	7.56663i	−0.145583	+	0.513656i
$218$	13.3666	−	7.71722i	0.905301	−	0.522676i
$219$	−13.0031	−	24.6055i	−0.878667	−	1.66269i
$220$	0.559189	−	0.322848i	0.0377005	−	0.0217664i
$221$	0.242460	−	0.139984i	0.0163096	−	0.00941637i
$222$	−2.52829	+	4.02339i	−0.169688	+	0.270032i
$223$	−17.3057	+	9.99144i	−1.15887	+	0.669076i	−0.951034	−	0.309087i	$-0.899977\pi$
$223$	−17.3057	+	9.99144i	−1.15887	+	0.669076i	−0.207840	+	0.978163i	$0.566643\pi$
$224$	0.721453	−	2.54549i	0.0482041	−	0.170078i
$225$	1.30143	+	2.70301i	0.0867619	+	0.180201i
$226$	1.57878	+	2.73453i	0.105019	+	0.181898i
$227$	15.6914			1.04147			0.520736	−	0.853718i	$-0.325658\pi$
$227$	15.6914			1.04147			0.520736	+	0.853718i	$0.325658\pi$
$228$	0.876605	+	1.65878i	0.0580546	+	0.109856i
$229$			11.1174i			0.734658i	0.930091	+	0.367329i	$0.119728\pi$
$229$			11.1174i			0.734658i	−0.930091	+	0.367329i	$0.880272\pi$
$230$	1.68335	−	2.91565i	0.110997	−	0.192252i
$231$	0.616754	+	2.89396i	0.0405794	+	0.190409i
$232$	1.70712	+	2.95682i	0.112078	+	0.194125i
$233$	19.8646	−	11.4688i	1.30137	−	0.751347i	0.320732	−	0.947170i	$-0.396071\pi$
$233$	19.8646	−	11.4688i	1.30137	−	0.751347i	0.980639	+	0.195823i	$0.0627378\pi$
$234$	0.450138	−	0.660115i	0.0294265	−	0.0431530i
$235$	−0.0268516	+	0.0465083i	−0.00175160	+	0.00303387i
$236$	2.85148	−	4.93891i	0.185616	−	0.321496i
$237$	6.61803	−	3.49738i	0.429887	−	0.227179i
$238$	0.758405	−	2.67586i	0.0491601	−	0.173450i
$239$	2.23325	+	1.28937i	0.144457	+	0.0834023i	0.570486	−	0.821307i	$-0.306755\pi$
$239$	2.23325	+	1.28937i	0.144457	+	0.0834023i	−0.426029	+	0.904709i	$0.640088\pi$
$240$	−1.53137	+	0.809270i	−0.0988493	+	0.0522381i
$241$		−	21.2682i		−	1.37000i	−0.728542	−	0.685002i	$-0.759802\pi$
$241$		−	21.2682i		−	1.37000i	0.728542	−	0.685002i	$-0.240198\pi$
$242$	9.16521	+	5.29154i	0.589162	+	0.340153i
$243$	−14.7147	+	5.14550i	−0.943951	+	0.330084i
$244$			3.54351i			0.226850i
$245$	0.201321	−	6.99710i	0.0128619	−	0.447029i
$246$	7.50825	+	0.281249i	0.478708	+	0.0179318i
$247$	−0.288488			−0.0183560
$248$	1.48628	+	2.57432i	0.0943791	+	0.163469i
$249$	0.237316	−	6.33539i	0.0150393	−	0.401489i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−20.0461			−1.26530			−0.632649	−	0.774439i	$-0.718032\pi$
$251$	−20.0461			−1.26530			−0.632649	+	0.774439i	$0.718032\pi$
$252$	−1.36267	−	7.81941i	−0.0858401	−	0.492576i
$253$	−2.17386			−0.136670
$254$	6.22187	+	3.59220i	0.390395	+	0.225395i
$255$	−1.60980	+	0.850719i	−0.100810	+	0.0532741i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.69654			−0.292962			−0.146481	−	0.989213i	$-0.546795\pi$
$257$	−4.69654			−0.292962			−0.146481	+	0.989213i	$0.546795\pi$
$258$	9.30338	−	14.8049i	0.579203	−	0.921712i
$259$	−6.98347	−	1.97929i	−0.433932	−	0.122987i
$260$		−	0.266328i		−	0.0165170i
$261$	8.46247	+	5.77064i	0.523814	+	0.357194i
$262$	−0.0647771	−	0.0373991i	−0.00400194	−	0.00231052i
$263$			12.1295i			0.747935i	0.927442	+	0.373968i	$0.122003\pi$
$263$			12.1295i			0.747935i	−0.927442	+	0.373968i	$0.877997\pi$
$264$	0.946934	+	0.595052i	0.0582797	+	0.0366229i
$265$	10.1657	+	5.86918i	0.624475	+	0.360541i
$266$	−2.05542	+	1.99714i	−0.126026	+	0.122452i
$267$	−0.793984	+	21.1962i	−0.0485910	+	1.29719i
$268$	3.61024	−	6.25312i	0.220531	−	0.381970i
$269$	4.72497	−	8.18388i	0.288086	−	0.498980i	−0.685267	−	0.728292i	$-0.740314\pi$
$269$	4.72497	−	8.18388i	0.288086	−	0.498980i	0.973353	+	0.229312i	$0.0736477\pi$
$270$	−3.08610	+	4.18043i	−0.187814	+	0.254413i
$271$	−0.709478	+	0.409617i	−0.0430977	+	0.0248825i	−0.521394	−	0.853316i	$-0.674588\pi$
$271$	−0.709478	+	0.409617i	−0.0430977	+	0.0248825i	0.478296	+	0.878199i	$0.341254\pi$
$272$	−0.525609	−	0.910381i	−0.0318697	−	0.0552000i
$273$	1.16094	+	0.376523i	0.0702631	+	0.0227882i
$274$	−3.92987	+	6.80673i	−0.237412	+	0.411210i
$275$		−	0.645696i		−	0.0389369i
$276$	5.82721	+	0.218280i	0.350757	+	0.0131389i
$277$	2.42014			0.145412			0.0727060	−	0.997353i	$-0.476837\pi$
$277$	2.42014			0.145412			0.0727060	+	0.997353i	$0.476837\pi$
$278$	−11.1774	−	19.3599i	−0.670379	−	1.16113i
$279$	7.36773	+	5.02413i	0.441095	+	0.300787i
$280$	−1.84373	−	1.89754i	−0.110184	−	0.113400i
$281$	−4.46431	+	2.57747i	−0.266318	+	0.153759i	−0.627213	−	0.778848i	$-0.715805\pi$
$281$	−4.46431	+	2.57747i	−0.266318	+	0.153759i	0.360895	+	0.932606i	$0.382471\pi$
$282$	−0.0929514	−	0.00348184i	−0.00553517	−	0.000207340i
$283$	−16.1042	+	9.29775i	−0.957294	+	0.552694i	−0.895339	−	0.445385i	$-0.853067\pi$
$283$	−16.1042	+	9.29775i	−0.957294	+	0.552694i	−0.0619545	+	0.998079i	$0.519733\pi$
$284$	−9.31536	+	5.37823i	−0.552765	+	0.319139i
$285$	1.87485	+	0.0702295i	0.111057	+	0.00416003i
$286$	−0.148928	+	0.0859835i	−0.00880629	+	0.00508431i
$287$	2.81075	+	11.1276i	0.165913	+	0.656840i
$288$	−2.47858	−	1.69016i	−0.146052	−	0.0995939i
$289$	7.94747	+	13.7654i	0.467498	+	0.809731i
$290$	3.41425			0.200491
$291$	−29.7260	−	1.11350i	−1.74257	−	0.0652744i
$292$		−	16.0677i		−	0.940290i
$293$	−13.5315	+	23.4372i	−0.790517	+	1.36922i	0.135130	+	0.990828i	$0.456855\pi$
$293$	−13.5315	+	23.4372i	−0.790517	+	1.36922i	−0.925647	+	0.378388i	$0.876478\pi$
$294$	10.8781	−	5.35425i	0.634421	−	0.312266i
$295$	−2.85148	−	4.93891i	−0.166020	−	0.287554i
$296$	−2.37592	+	1.37174i	−0.138097	+	0.0797305i
$297$	3.33399	+	0.376069i	0.193458	+	0.0218217i
$298$	7.85703	−	13.6088i	0.455146	−	0.788335i
$299$	−0.448323	+	0.776519i	−0.0259272	+	0.0449072i
$300$	−0.0648349	+	1.73084i	−0.00374325	+	0.0999299i
$301$	25.6971	+	7.28319i	1.48116	+	0.419796i
$302$	5.59974	+	3.23301i	0.322229	+	0.186039i
$303$	0.657874	+	0.413408i	0.0377939	+	0.0237497i
$304$			1.08320i			0.0621260i
$305$	3.06877	+	1.77175i	0.175717	+	0.101450i
$306$	−2.60552	−	1.77673i	−0.148948	−	0.101569i
$307$			26.5519i			1.51539i	0.652606	+	0.757697i	$0.273676\pi$
$307$			26.5519i			1.51539i	−0.652606	+	0.757697i	$0.726324\pi$
$308$	−0.465840	+	1.64361i	−0.0265437	+	0.0936535i
$309$	5.22477	−	8.31441i	0.297227	−	0.472990i
$310$	2.97257			0.168830
$311$	7.18458	+	12.4441i	0.407400	+	0.705638i	0.994598	−	0.103806i	$-0.0331021\pi$
$311$	7.18458	+	12.4441i	0.407400	+	0.705638i	−0.587197	+	0.809444i	$0.699769\pi$
$312$	0.407846	−	0.215531i	0.0230897	−	0.0122021i
$313$	−9.50068	−	5.48522i	−0.537010	−	0.310043i	0.206856	−	0.978371i	$-0.433677\pi$
$313$	−9.50068	−	5.48522i	−0.537010	−	0.310043i	−0.743866	+	0.668328i	$0.767010\pi$
$314$	−15.2110			−0.858408
$315$	−7.45314	−	2.72960i	−0.419937	−	0.153795i
$316$	4.32165			0.243112
$317$	14.4451	+	8.33988i	0.811317	+	0.468414i	0.847413	−	0.530934i	$-0.178159\pi$
$317$	14.4451	+	8.33988i	0.811317	+	0.468414i	−0.0360960	+	0.999348i	$0.511492\pi$
$318$	−0.761055	+	20.3172i	−0.0426779	+	1.13933i
$319$	−1.10228	−	1.90921i	−0.0617160	−	0.106895i
$320$	−1.00000			−0.0559017
$321$	6.63767	+	0.248639i	0.370479	+	0.0138776i
$322$	2.18144	+	8.63620i	0.121567	+	0.481277i
$323$			1.13868i			0.0633580i
$324$	−8.89926	−	1.34285i	−0.494403	−	0.0746028i
$325$	−0.230647	−	0.133164i	−0.0127940	−	0.00738661i
$326$		−	10.6497i		−	0.589832i
$327$	23.6358	−	12.4906i	1.30706	−	0.690733i
$328$	3.75676	+	2.16896i	0.207432	+	0.119761i
$329$	−0.0347968	−	0.137758i	−0.00191841	−	0.00759487i
$330$	0.988797	−	0.522542i	0.0544315	−	0.0287650i
$331$	2.77401	−	4.80472i	0.152473	−	0.264091i	−0.779663	−	0.626199i	$-0.784610\pi$
$331$	2.77401	−	4.80472i	0.152473	−	0.264091i	0.932136	+	0.362108i	$0.117943\pi$
$332$	1.83015	−	3.16992i	0.100443	−	0.173972i
$333$	−4.63692	+	6.79991i	−0.254102	+	0.372633i
$334$	−17.1424	+	9.89716i	−0.937989	+	0.541548i
$335$	−3.61024	−	6.25312i	−0.197249	−	0.341645i
$336$	1.41375	−	4.35905i	0.0771266	−	0.237806i
$337$	−15.3125	+	26.5220i	−0.834125	+	1.44475i	0.0606161	+	0.998161i	$0.480693\pi$
$337$	−15.3125	+	26.5220i	−0.834125	+	1.44475i	−0.894741	+	0.446586i	$0.852640\pi$
$338$		−	12.9291i		−	0.703249i
$339$	2.55532	+	4.83539i	0.138786	+	0.262622i
$340$	−1.05122			−0.0570103
$341$	−0.959687	−	1.66223i	−0.0519700	−	0.0900147i
$342$	1.40971	+	2.92792i	0.0762285	+	0.158324i
$343$	12.5188	+	13.6485i	0.675949	+	0.736948i
$344$	8.74267	−	5.04758i	0.471373	−	0.272148i
$345$	3.10264	−	4.93737i	0.167040	−	0.265819i
$346$	12.1859	−	7.03552i	0.655116	−	0.378232i
$347$	−31.6290	+	18.2610i	−1.69793	+	0.980301i	−0.750212	+	0.661197i	$0.770049\pi$
$347$	−31.6290	+	18.2610i	−1.69793	+	0.980301i	−0.947720	+	0.319104i	$0.896618\pi$
$348$	2.76305	+	5.22846i	0.148115	+	0.280275i
$349$	0.811147	−	0.468316i	0.0434197	−	0.0250684i	−0.478133	−	0.878287i	$-0.658686\pi$
$349$	0.811147	−	0.468316i	0.0434197	−	0.0250684i	0.521553	+	0.853219i	$0.325353\pi$
$350$	−2.56518	+	0.647947i	−0.137115	+	0.0346342i
$351$	0.821915	−	1.11337i	0.0438706	−	0.0594271i
$352$	0.322848	+	0.559189i	0.0172079	+	0.0298049i
$353$	8.33225			0.443481			0.221741	−	0.975106i	$-0.428826\pi$
$353$	8.33225			0.443481			0.221741	+	0.975106i	$0.428826\pi$
$354$	5.25566	−	8.36357i	0.279335	−	0.444519i
$355$			10.7565i			0.570893i
$356$	−6.12312	+	10.6056i	−0.324525	+	0.562093i
$357$	1.48616	−	4.58231i	0.0786561	−	0.242521i
$358$	6.93177	+	12.0062i	0.366355	+	0.634546i
$359$	−20.1878	+	11.6555i	−1.06547	+	0.615152i	−0.926941	−	0.375206i	$-0.877572\pi$
$359$	−20.1878	+	11.6555i	−1.06547	+	0.615152i	−0.138532	+	0.990358i	$0.544239\pi$
$360$	−2.70301	+	1.30143i	−0.142461	+	0.0685913i
$361$	−8.91333	+	15.4383i	−0.469123	+	0.812545i
$362$	−4.91386	+	8.51106i	−0.258267	+	0.447332i
$363$	15.5204	+	9.75302i	0.814610	+	0.511901i
$364$	0.491037	+	0.505368i	0.0257373	+	0.0264885i
$365$	−13.9150	−	8.03384i	−0.728345	−	0.420510i
$366$	−0.229743	+	6.13324i	−0.0120089	+	0.320589i
$367$			4.49651i			0.234716i	0.993090	+	0.117358i	$0.0374425\pi$
$367$			4.49651i			0.234716i	−0.993090	+	0.117358i	$0.962558\pi$
$368$	2.91565	+	1.68335i	0.151989	+	0.0877507i
$369$	12.9773	+	0.973593i	0.675572	+	0.0506832i
$370$			2.74347i			0.142626i
$371$	−30.1110	+	7.60583i	−1.56329	+	0.394875i
$372$	2.40561	+	4.55209i	0.124725	+	0.236015i
$373$	31.1446			1.61261			0.806303	−	0.591503i	$-0.201465\pi$
$373$	31.1446			1.61261			0.806303	+	0.591503i	$0.201465\pi$
$374$	0.339384	+	0.587830i	0.0175491	+	0.0303959i
$375$	1.46653	+	0.921567i	0.0757313	+	0.0475895i
$376$	−0.0465083	−	0.0268516i	−0.00239848	−	0.00138476i
$377$	−0.909310			−0.0468318
$378$	−1.85159	−	13.6225i	−0.0952354	−	0.700664i
$379$	7.02139			0.360664			0.180332	−	0.983606i	$-0.442283\pi$
$379$	7.02139			0.360664			0.180332	+	0.983606i	$0.442283\pi$
$380$	0.938083	+	0.541602i	0.0481226	+	0.0277836i
$381$	10.5361	+	6.62091i	0.539783	+	0.339199i
$382$	−9.52928	−	16.5052i	−0.487560	−	0.844479i
$383$	−15.9236			−0.813657			−0.406828	−	0.913505i	$-0.633365\pi$
$383$	−15.9236			−0.813657			−0.406828	+	0.913505i	$0.633365\pi$
$384$	−0.809270	−	1.53137i	−0.0412979	−	0.0781472i
$385$	1.19049	+	1.22523i	0.0606730	+	0.0624437i
$386$			14.5664i			0.741412i
$387$	17.0625	−	25.0217i	0.867336	−	1.27192i
$388$	−14.8734	−	8.58718i	−0.755084	−	0.435948i
$389$			8.94395i			0.453476i	0.973956	+	0.226738i	$0.0728062\pi$
$389$			8.94395i			0.453476i	−0.973956	+	0.226738i	$0.927194\pi$
$390$	0.0172674	−	0.460970i	0.000874367	−	0.0233421i
$391$	3.06498	+	1.76957i	0.155003	+	0.0894908i
$392$	6.99710	+	0.201321i	0.353407	+	0.0101682i
$393$	−0.109694	−	0.0689316i	−0.00553332	−	0.00347714i
$394$	−9.05884	+	15.6904i	−0.456378	+	0.790469i
$395$	2.16082	−	3.74266i	0.108723	−	0.188314i
$396$	1.60041	+	1.09133i	0.0804235	+	0.0548415i
$397$	−1.35910	+	0.784676i	−0.0682112	+	0.0393818i	−0.533718	−	0.845663i	$-0.679206\pi$
$397$	−1.35910	+	0.784676i	−0.0682112	+	0.0393818i	0.465507	+	0.885044i	$0.345872\pi$
$398$	−7.79625	−	13.5035i	−0.390791	−	0.676869i
$399$	−3.68709	+	3.32345i	−0.184585	+	0.166381i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	33.8403i		−	1.68991i	−0.534840	−	0.844953i	$-0.679628\pi$
$401$		−	33.8403i		−	1.68991i	0.534840	−	0.844953i	$-0.320372\pi$
$402$	6.65416	−	10.5891i	0.331879	−	0.528135i
$403$	−0.791678			−0.0394363
$404$	0.224296	+	0.388492i	0.0111591	+	0.0193282i
$405$	−5.61257	+	7.03556i	−0.278891	+	0.349600i
$406$	−6.47867	+	6.29495i	−0.321531	+	0.312413i
$407$	1.53412	−	0.885725i	0.0760435	−	0.0439037i
$408$	−0.850719	−	1.60980i	−0.0421168	−	0.0796969i
$409$	7.47355	−	4.31486i	0.369543	−	0.213356i	−0.303716	−	0.952763i	$-0.598227\pi$
$409$	7.47355	−	4.31486i	0.369543	−	0.213356i	0.673259	+	0.739407i	$0.264894\pi$
$410$	3.75676	−	2.16896i	0.185533	−	0.107118i
$411$	−7.24328	+	11.5266i	−0.357284	+	0.568563i
$412$	4.90988	−	2.83472i	0.241892	−	0.139657i
$413$	14.5168	+	4.11442i	0.714326	+	0.202457i
$414$	10.0718	+	0.755613i	0.495002	+	0.0371363i
$415$	−1.83015	−	3.16992i	−0.0898386	−	0.155605i
$416$	0.266328			0.0130578
$417$	−18.0911	−	34.2335i	−0.885927	−	1.67642i
$418$		−	0.699421i		−	0.0342098i
$419$	−6.77897	+	11.7415i	−0.331174	+	0.573610i	−0.982742	−	0.184980i	$-0.940778\pi$
$419$	−6.77897	+	11.7415i	−0.331174	+	0.573610i	0.651568	+	0.758590i	$0.274111\pi$
$420$	−3.06817	−	3.40387i	−0.149711	−	0.166092i
$421$	−1.64981	−	2.85756i	−0.0804069	−	0.139269i	0.823018	−	0.568015i	$-0.192289\pi$
$421$	−1.64981	−	2.85756i	−0.0804069	−	0.139269i	−0.903425	+	0.428747i	$0.858955\pi$
$422$	−2.86818	+	1.65595i	−0.139621	+	0.0806102i
$423$	−0.160658	−	0.0120530i	−0.00781146	−	0.000586036i
$424$	−5.86918	+	10.1657i	−0.285032	+	0.493691i
$425$	−0.525609	+	0.910381i	−0.0254958	+	0.0441600i
$426$	−16.4721	+	8.70487i	−0.798074	+	0.421752i
$427$	−9.08975	+	2.29600i	−0.439884	+	0.111111i
$428$	3.32116	+	1.91747i	0.160534	+	0.0926846i
$429$	−0.263345	+	0.139168i	−0.0127144	+	0.00671908i
$430$		−	10.0952i		−	0.486832i
$431$	−17.0763	−	9.85901i	−0.822537	−	0.474892i	0.0287538	−	0.999587i	$-0.490846\pi$
$431$	−17.0763	−	9.85901i	−0.822537	−	0.474892i	−0.851290	+	0.524695i	$0.824179\pi$
$432$	−4.18043	−	3.08610i	−0.201131	−	0.148480i
$433$			4.54514i			0.218426i	0.994018	+	0.109213i	$0.0348330\pi$
$433$			4.54514i			0.218426i	−0.994018	+	0.109213i	$0.965167\pi$
$434$	−5.64056	+	5.48061i	−0.270756	+	0.263078i
$435$	5.90950	+	0.221362i	0.283339	+	0.0106135i
$436$	15.4344			0.739175
$437$	−1.82341	−	3.15824i	−0.0872256	−	0.151079i
$438$	1.04175	−	27.8105i	0.0497766	−	1.32884i
$439$	15.0163	+	8.66968i	0.716691	+	0.413781i	0.813533	−	0.581518i	$-0.197541\pi$
$439$	15.0163	+	8.66968i	0.716691	+	0.413781i	−0.0968429	+	0.995300i	$0.530874\pi$
$440$	0.645696			0.0307824
$441$	19.1753	−	8.56206i	0.913108	−	0.407717i
$442$	0.279969			0.0133168
$443$	−0.850958	−	0.491301i	−0.0404302	−	0.0233424i	0.479649	−	0.877461i	$-0.340764\pi$
$443$	−0.850958	−	0.491301i	−0.0404302	−	0.0233424i	−0.520079	+	0.854118i	$0.674097\pi$
$444$	−4.20126	+	2.22021i	−0.199383	+	0.105366i
$445$	6.12312	+	10.6056i	0.290264	+	0.502752i
$446$	−19.9829			−0.946217
$447$	14.4816	−	23.0452i	0.684955	−	1.09000i
$448$	1.89754	−	1.84373i	0.0896504	−	0.0871080i
$449$			29.6441i			1.39899i	0.714636	+	0.699496i	$0.246592\pi$
$449$			29.6441i			1.39899i	−0.714636	+	0.699496i	$0.753408\pi$
$450$	−0.224437	+	2.99159i	−0.0105801	+	0.141025i
$451$	−2.42572	−	1.40049i	−0.114223	−	0.0659466i
$452$			3.15757i			0.148519i
$453$	9.48262	+	5.95887i	0.445533	+	0.279972i
$454$	13.5891	+	7.84568i	0.637769	+	0.368216i
$455$	0.683180	−	0.172566i	0.0320280	−	0.00809004i
$456$	−0.0702295	+	1.87485i	−0.00328880	+	0.0877979i
$457$	5.85157	−	10.1352i	0.273725	−	0.474106i	−0.696088	−	0.717957i	$-0.745077\pi$
$457$	5.85157	−	10.1352i	0.273725	−	0.474106i	0.969813	+	0.243851i	$0.0784108\pi$
$458$	−5.55869	+	9.62794i	−0.259741	+	0.449884i
$459$	−4.39454	−	3.24416i	−0.205120	−	0.151424i
$460$	2.91565	−	1.68335i	0.135943	−	0.0784866i
$461$	−18.2593	−	31.6260i	−0.850418	−	1.47297i	−0.880831	−	0.473430i	$-0.843016\pi$
$461$	−18.2593	−	31.6260i	−0.850418	−	1.47297i	0.0304133	−	0.999537i	$-0.490318\pi$
$462$	−0.912856	+	2.81462i	−0.0424699	+	0.130948i
$463$	−1.08855	+	1.88543i	−0.0505893	+	0.0876233i	−0.890211	−	0.455548i	$-0.849443\pi$
$463$	−1.08855	+	1.88543i	−0.0505893	+	0.0876233i	0.839622	+	0.543171i	$0.182777\pi$
$464$			3.41425i			0.158502i
$465$	5.14503	+	0.192726i	0.238595	+	0.00893746i
$466$	22.9376			1.06257
$467$	−12.2781	−	21.2663i	−0.568164	−	0.984088i	−0.996748	−	0.0805862i	$-0.974321\pi$
$467$	−12.2781	−	21.2663i	−0.568164	−	0.984088i	0.428584	−	0.903502i	$-0.359013\pi$
$468$	0.719889	−	0.346607i	0.0332769	−	0.0160219i
$469$	18.3797	+	5.20924i	0.848693	+	0.240541i
$470$	−0.0465083	+	0.0268516i	−0.00214527	+	0.00123857i
$471$	−26.3278	−	0.986206i	−1.21312	−	0.0454420i
$472$	4.93891	−	2.85148i	0.227332	−	0.131250i
$473$	−5.64511	+	3.25921i	−0.259562	+	0.149858i
$474$	7.48007	+	0.280194i	0.343571	+	0.0128697i
$475$	0.938083	−	0.541602i	0.0430422	−	0.0248504i
$476$	1.99473	−	1.93816i	0.0914282	−	0.0888355i
$477$	−2.63452	+	35.1164i	−0.120627	+	1.60787i
$478$	1.28937	+	2.23325i	0.0589743	+	0.102147i
$479$	30.1072			1.37563			0.687816	−	0.725885i	$-0.258570\pi$
$479$	30.1072			1.37563			0.687816	+	0.725885i	$0.258570\pi$
$480$	−1.73084	−	0.0648349i	−0.0790015	−	0.00295930i
$481$		−	0.730664i		−	0.0333154i
$482$	10.6341	−	18.4188i	0.484369	−	0.838952i
$483$	3.21579	+	15.0893i	0.146324	+	0.686586i
$484$	5.29154	+	9.16521i	0.240524	+	0.416601i
$485$	−14.8734	+	8.58718i	−0.675368	+	0.389924i
$486$	−15.3161	−	2.90124i	−0.694752	−	0.131603i
$487$	11.3594	−	19.6750i	0.514742	−	0.891560i	−0.485111	−	0.874452i	$-0.661221\pi$
$487$	11.3594	−	19.6750i	0.514742	−	0.891560i	0.999854	−	0.0171073i	$-0.00544569\pi$
$488$	−1.77175	+	3.06877i	−0.0802035	+	0.138917i
$489$	0.690472	−	18.4329i	0.0312242	−	0.833564i
$490$	3.67290	−	5.95901i	0.165925	−	0.269201i
$491$	−15.8571	−	9.15511i	−0.715621	−	0.413164i	0.0975175	−	0.995234i	$-0.468910\pi$
$491$	−15.8571	−	9.15511i	−0.715621	−	0.413164i	−0.813139	+	0.582070i	$0.802243\pi$
$492$	6.36171	+	3.99769i	0.286808	+	0.180230i
$493$			3.58912i			0.161646i
$494$	−0.249838	−	0.144244i	−0.0112407	−	0.00648984i
$495$	1.74533	−	0.840327i	0.0784466	−	0.0377699i
$496$			2.97257i			0.133472i
$497$	−19.8320	−	20.4108i	−0.889586	−	0.915550i
$498$	3.37322	−	5.36795i	0.151157	−	0.240544i
$499$	−22.8391			−1.02242			−0.511210	−	0.859456i	$-0.670802\pi$
$499$	−22.8391			−1.02242			−0.511210	+	0.859456i	$0.670802\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−30.3124	+	16.0189i	−1.35426	+	0.715674i
$502$	−17.3604	−	10.0230i	−0.774833	−	0.447350i
$503$	−17.5765			−0.783699			−0.391849	−	0.920029i	$-0.628165\pi$
$503$	−17.5765			−0.783699			−0.391849	+	0.920029i	$0.628165\pi$
$504$	2.72960	−	7.45314i	0.121586	−	0.331989i
$505$	0.448592			0.0199621
$506$	−1.88262	−	1.08693i	−0.0836928	−	0.0483200i
$507$	0.838255	−	22.3781i	0.0372282	−	0.993847i
$508$	3.59220	+	6.22187i	0.159378	+	0.276051i
$509$	38.2842			1.69692			0.848458	−	0.529262i	$-0.177531\pi$
$509$	38.2842			1.69692			0.848458	+	0.529262i	$0.177531\pi$
$510$	−1.81949	−	0.0681556i	−0.0805682	−	0.00301798i
$511$	41.2166	−	10.4110i	1.82331	−	0.460556i
$512$		−	1.00000i		−	0.0441942i
$513$	2.25015	+	5.15915i	0.0993466	+	0.227782i
$514$	−4.06732	−	2.34827i	−0.179402	−	0.103578i
$515$		−	5.66944i		−	0.249825i
$516$	15.4594	−	8.16972i	0.680562	−	0.359652i
$517$	0.0300302	+	0.0173380i	0.00132073	+	0.000762522i
$518$	−5.05822	−	5.20585i	−0.222245	−	0.228732i
$519$	21.5479	−	11.3873i	0.945848	−	0.499845i
$520$	0.133164	−	0.230647i	0.00583963	−	0.0101145i
$521$	4.81631	−	8.34209i	0.211006	−	0.365474i	−0.741023	−	0.671479i	$-0.765659\pi$
$521$	4.81631	−	8.34209i	0.211006	−	0.365474i	0.952030	+	0.306006i	$0.0989926\pi$
$522$	4.44340	+	9.22876i	0.194482	+	0.403932i
$523$	15.4244	−	8.90530i	0.674463	−	0.389401i	−0.123303	−	0.992369i	$-0.539349\pi$
$523$	15.4244	−	8.90530i	0.674463	−	0.389401i	0.797766	+	0.602968i	$0.206015\pi$
$524$	−0.0373991	−	0.0647771i	−0.00163379	−	0.00282980i
$525$	−4.48192	+	0.955176i	−0.195607	+	0.0416873i
$526$	−6.06474	+	10.5044i	−0.264435	+	0.458015i
$527$			3.12481i			0.136119i
$528$	0.522542	+	0.988797i	0.0227407	+	0.0430319i
$529$	11.6653			0.507189
$530$	5.86918	+	10.1657i	0.254941	+	0.441570i
$531$	9.63894	−	14.1352i	0.418295	−	0.613417i
$532$	−2.77862	+	0.701859i	−0.120468	+	0.0304294i
$533$	−1.00053	+	0.577656i	−0.0433378	+	0.0250211i
$534$	−11.2857	+	17.9595i	−0.488382	+	0.777184i
$535$	3.32116	−	1.91747i	0.143586	−	0.0828996i
$536$	6.25312	−	3.61024i	0.270094	−	0.155939i
$537$	11.2193	+	21.2301i	0.484150	+	0.916149i
$538$	8.18388	−	4.72497i	0.352832	−	0.203708i
$539$	−4.51800	−	0.129992i	−0.194604	−	0.00559915i
$540$	−4.76285	+	2.07731i	−0.204961	+	0.0893932i
$541$	16.5362	+	28.6415i	0.710945	+	1.23139i	0.964503	+	0.264073i	$0.0850658\pi$
$541$	16.5362	+	28.6415i	0.710945	+	1.23139i	−0.253558	+	0.967320i	$0.581601\pi$
$542$	−0.819235			−0.0351891
$543$	−9.05691	+	14.4127i	−0.388669	+	0.618507i
$544$		−	1.05122i		−	0.0450706i
$545$	7.71722	−	13.3666i	0.330569	−	0.572563i
$546$	0.817140	+	0.906547i	0.0349703	+	0.0387966i
$547$	−5.28847	−	9.15990i	−0.226119	−	0.391649i	0.730536	−	0.682874i	$-0.239270\pi$
$547$	−5.28847	−	9.15990i	−0.226119	−	0.391649i	−0.956654	+	0.291225i	$0.905937\pi$
$548$	−6.80673	+	3.92987i	−0.290769	+	0.167876i
$549$	−0.795296	+	10.6007i	−0.0339424	+	0.452428i
$550$	0.322848	−	0.559189i	0.0137663	−	0.0238439i
$551$	1.84916	−	3.20285i	0.0787770	−	0.136446i
$552$	4.93737	+	3.10264i	0.210148	+	0.132057i
$553$	2.80020	+	11.0858i	0.119077	+	0.471417i
$554$	2.09590	+	1.21007i	0.0890463	+	0.0514109i
$555$	−0.177873	+	4.74850i	−0.00755028	+	0.201563i
$556$		−	22.3549i		−	0.948058i
$557$	−6.46701	−	3.73373i	−0.274016	−	0.158203i	0.356695	−	0.934221i	$-0.383903\pi$
$557$	−6.46701	−	3.73373i	−0.274016	−	0.158203i	−0.630711	+	0.776018i	$0.717237\pi$
$558$	3.86858	+	8.03489i	0.163770	+	0.340144i
$559$			2.68863i			0.113717i
$560$	−0.647947	−	2.56518i	−0.0273807	−	0.108399i
$561$	0.549306	+	1.03944i	0.0231917	+	0.0438852i
$562$	−5.15494			−0.217448
$563$	7.66915	+	13.2834i	0.323216	+	0.559827i	0.981150	−	0.193249i	$-0.0619026\pi$
$563$	7.66915	+	13.2834i	0.323216	+	0.559827i	−0.657934	+	0.753076i	$0.728569\pi$
$564$	−0.0787573	−	0.0494910i	−0.00331628	−	0.00208395i
$565$	2.73453	+	1.57878i	0.115043	+	0.0664199i
$566$	−18.5955			−0.781627
$567$	−2.32159	−	23.6983i	−0.0974974	−	0.995236i
$568$	−10.7565			−0.451331
$569$	−0.784849	−	0.453133i	−0.0329026	−	0.0189963i	0.483458	−	0.875367i	$-0.339380\pi$
$569$	−0.784849	−	0.453133i	−0.0329026	−	0.0189963i	−0.516361	+	0.856371i	$0.672714\pi$
$570$	1.58855	+	0.998246i	0.0665372	+	0.0418119i
$571$	−17.7429	−	30.7315i	−0.742516	−	1.28607i	−0.951346	−	0.308123i	$-0.900299\pi$
$571$	−17.7429	−	30.7315i	−0.742516	−	1.28607i	0.208831	−	0.977952i	$-0.433034\pi$
$572$	−0.171967			−0.00719030
$573$	−15.4235	−	29.1856i	−0.644326	−	1.21925i
$574$	−3.12961	+	11.0421i	−0.130628	+	0.460890i
$575$		−	3.36670i		−	0.140401i
$576$	−1.30143	−	2.70301i	−0.0542262	−	0.112626i
$577$	−25.7446	−	14.8636i	−1.07176	−	0.618781i	−0.143098	−	0.989709i	$-0.545706\pi$
$577$	−25.7446	−	14.8636i	−1.07176	−	0.618781i	−0.928662	+	0.370928i	$0.879040\pi$
$578$			15.8949i			0.661142i
$579$	−0.944414	+	25.2121i	−0.0392485	+	1.04778i
$580$	2.95682	+	1.70712i	0.122775	+	0.0708844i
$581$	9.31726	+	2.64074i	0.386545	+	0.109556i
$582$	−25.1867	−	15.8273i	−1.04402	−	0.656064i
$583$	3.78971	−	6.56396i	0.156954	−	0.271852i
$584$	8.03384	−	13.9150i	0.332443	−	0.575808i
$585$	0.0597740	−	0.796745i	0.00247135	−	0.0329414i
$586$	−23.4372	+	13.5315i	−0.968182	+	0.558980i
$587$	15.2602	+	26.4315i	0.629857	+	1.09095i	0.987580	+	0.157117i	$0.0502200\pi$
$587$	15.2602	+	26.4315i	0.629857	+	1.09095i	−0.357723	+	0.933828i	$0.616447\pi$
$588$	12.0978	+	0.802110i	0.498905	+	0.0330785i
$589$	1.60995	−	2.78851i	0.0663368	−	0.114899i
$590$		−	5.70296i		−	0.234787i
$591$	−16.6966	+	26.5701i	−0.686808	+	1.09295i
$592$	−2.74347			−0.112756
$593$	−15.1799	−	26.2924i	−0.623366	−	1.07970i	−0.988854	−	0.148885i	$-0.952432\pi$
$593$	−15.1799	−	26.2924i	−0.623366	−	1.07970i	0.365489	−	0.930816i	$-0.380902\pi$
$594$	2.69929	+	1.99268i	0.110753	+	0.0817607i
$595$	−0.681133	−	2.69657i	−0.0279237	−	0.110548i
$596$	13.6088	−	7.85703i	0.557437	−	0.321837i
$597$	−12.6185	−	23.8778i	−0.516442	−	0.977254i
$598$	−0.776519	+	0.448323i	−0.0317542	+	0.0183333i
$599$	−6.15334	+	3.55263i	−0.251419	+	0.145157i	−0.620414	−	0.784275i	$-0.713035\pi$
$599$	−6.15334	+	3.55263i	−0.251419	+	0.145157i	0.368995	+	0.929431i	$0.379702\pi$
$600$	−0.921567	+	1.46653i	−0.0376228	+	0.0598709i
$601$	22.8386	−	13.1859i	0.931607	−	0.537864i	0.0442879	−	0.999019i	$-0.485898\pi$
$601$	22.8386	−	13.1859i	0.931607	−	0.537864i	0.887320	+	0.461155i	$0.152565\pi$
$602$	18.6128	+	19.1560i	0.758600	+	0.780740i
$603$	12.2038	−	17.8965i	0.496978	−	0.728803i
$604$	3.23301	+	5.59974i	0.131549	+	0.227850i
$605$	10.5831			0.430263
$606$	0.363032	+	0.686959i	0.0147472	+	0.0279058i
$607$		−	3.86727i		−	0.156968i	−0.996915	−	0.0784839i	$-0.974992\pi$
$607$		−	3.86727i		−	0.156968i	0.996915	−	0.0784839i	$-0.0250079\pi$
$608$	−0.541602	+	0.938083i	−0.0219649	+	0.0380443i
$609$	−11.6217	+	10.4755i	−0.470933	+	0.424488i
$610$	1.77175	+	3.06877i	0.0717362	+	0.124251i
$611$	0.0123865	−	0.00715133i	0.000501103	−	0.000289312i
$612$	−1.36808	−	2.84146i	−0.0553015	−	0.114859i
$613$	10.4441	−	18.0897i	0.421833	−	0.730637i	−0.574286	−	0.818655i	$-0.694720\pi$
$613$	10.4441	−	18.0897i	0.421833	−	0.730637i	0.996119	+	0.0880184i	$0.0280534\pi$
$614$	−13.2759	+	22.9946i	−0.535773	+	0.927986i
$615$	6.64296	−	3.51055i	0.267870	−	0.141559i
$616$	−1.22523	+	1.19049i	−0.0493661	+	0.0479662i
$617$	−34.0270	−	19.6455i	−1.36987	−	0.790898i	−0.378963	−	0.925412i	$-0.623719\pi$
$617$	−34.0270	−	19.6455i	−1.36987	−	0.790898i	−0.990912	+	0.134514i	$0.957053\pi$
$618$	8.68199	−	4.58811i	0.349241	−	0.184561i
$619$		−	8.31333i		−	0.334141i	−0.985945	−	0.167071i	$-0.946569\pi$
$619$		−	8.31333i		−	0.334141i	0.985945	−	0.167071i	$-0.0534308\pi$
$620$	2.57432	+	1.48628i	0.103387	+	0.0596906i
$621$	17.3836	+	1.96085i	0.697581	+	0.0786861i
$622$			14.3692i			0.576151i
$623$	−31.1727	−	8.83509i	−1.24891	−	0.353971i
$624$	0.460970	+	0.0172674i	0.0184536	+	0.000691248i
$625$	1.00000			0.0400000
$626$	−5.48522	−	9.50068i	−0.219234	−	0.379724i
$627$	0.0453469	−	1.21058i	0.00181098	−	0.0483461i
$628$	−13.1731	−	7.60552i	−0.525666	−	0.303493i
$629$	−2.88399			−0.114992
$630$	−5.08981	−	6.09047i	−0.202783	−	0.242650i
$631$	11.0713			0.440743			0.220372	−	0.975416i	$-0.429273\pi$
$631$	11.0713			0.440743			0.220372	+	0.975416i	$0.429273\pi$
$632$	3.74266	+	2.16082i	0.148875	+	0.0859530i
$633$	−5.07172	+	2.68021i	−0.201583	+	0.106529i
$634$	8.33988	+	14.4451i	0.331219	+	0.573688i
$635$	7.18440			0.285104
$636$	−10.8177	+	17.2147i	−0.428949	+	0.682606i
$637$	−0.978197	+	1.58705i	−0.0387576	+	0.0628813i
$638$		−	2.20457i		−	0.0872796i
$639$	−29.0748	+	13.9987i	−1.15018	+	0.553782i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	30.8884i		−	1.22002i	−0.792394	−	0.610010i	$-0.791166\pi$
$641$		−	30.8884i		−	1.22002i	0.792394	−	0.610010i	$-0.208834\pi$
$642$	5.62407	+	3.53416i	0.221964	+	0.139482i
$643$	−14.7423	−	8.51146i	−0.581379	−	0.335659i	0.180302	−	0.983611i	$-0.442292\pi$
$643$	−14.7423	−	8.51146i	−0.581379	−	0.335659i	−0.761681	+	0.647952i	$0.775626\pi$
$644$	−2.42892	+	8.56989i	−0.0957127	+	0.337701i
$645$	0.654519	−	17.4731i	0.0257717	−	0.688002i
$646$	−0.569342	+	0.986129i	−0.0224005	+	0.0387987i
$647$	22.3824	−	38.7675i	0.879944	−	1.52411i	0.0285419	−	0.999593i	$-0.490914\pi$
$647$	22.3824	−	38.7675i	0.879944	−	1.52411i	0.851402	−	0.524514i	$-0.175753\pi$
$648$	−7.03556	−	5.61257i	−0.276383	−	0.220483i
$649$	−3.18903	+	1.84119i	−0.125181	+	0.0722730i
$650$	−0.133164	−	0.230647i	−0.00522312	−	0.00904672i
$651$	−10.1182	+	9.12033i	−0.396565	+	0.357454i
$652$	5.32485	−	9.22290i	0.208537	−	0.361197i
$653$			13.7987i			0.539985i	0.962862	+	0.269993i	$0.0870213\pi$
$653$			13.7987i			0.539985i	−0.962862	+	0.269993i	$0.912979\pi$
$654$	26.7145	+	1.00069i	1.04462	+	0.0391301i
$655$	−0.0747982			−0.00292261
$656$	2.16896	+	3.75676i	0.0846838	+	0.146677i
$657$	3.60619	−	48.0680i	0.140691	−	1.87531i
$658$	0.0387443	−	0.136701i	0.00151041	−	0.00532915i
$659$	39.8972	−	23.0347i	1.55417	−	0.897303i	0.556379	−	0.830928i	$-0.312190\pi$
$659$	39.8972	−	23.0347i	1.55417	−	0.897303i	0.997795	−	0.0663746i	$-0.0211432\pi$
$660$	1.11759	+	0.0418637i	0.0435023	+	0.00162954i
$661$	−13.0963	+	7.56114i	−0.509386	+	0.294094i	−0.732581	−	0.680679i	$-0.761685\pi$
$661$	−13.0963	+	7.56114i	−0.509386	+	0.294094i	0.223195	+	0.974774i	$0.428351\pi$
$662$	4.80472	−	2.77401i	0.186741	−	0.107815i
$663$	0.484580	+	0.0181518i	0.0188195	+	0.000704956i
$664$	3.16992	−	1.83015i	0.123017	−	0.0710237i
$665$	−0.781482	+	2.75728i	−0.0303046	+	0.106923i
$666$	−7.41564	+	3.57043i	−0.287350	+	0.138351i
$667$	−5.74737	−	9.95474i	−0.222539	−	0.385449i
$668$	−19.7943			−0.765865
$669$	−34.5871	−	1.29559i	−1.33721	−	0.0500903i
$670$		−	7.22048i		−	0.278952i
$671$	1.14402	−	1.98149i	0.0441642	−	0.0764947i
$672$	3.40387	−	3.06817i	0.131307	−	0.118357i
$673$	−24.9981	−	43.2980i	−0.963607	−	1.66902i	−0.713311	−	0.700848i	$-0.752805\pi$
$673$	−24.9981	−	43.2980i	−0.963607	−	1.66902i	−0.250296	−	0.968169i	$-0.580528\pi$
$674$	−26.5220	+	15.3125i	−1.02159	+	0.589815i
$675$	−0.582424	+	5.16341i	−0.0224175	+	0.198740i
$676$	6.46453	−	11.1969i	0.248636	−	0.430650i
$677$	7.48230	−	12.9597i	0.287568	−	0.498083i	−0.685661	−	0.727921i	$-0.740487\pi$
$677$	7.48230	−	12.9597i	0.287568	−	0.498083i	0.973229	+	0.229839i	$0.0738199\pi$
$678$	−0.204721	+	5.46523i	−0.00786225	+	0.209891i
$679$	12.3905	−	43.7171i	0.475504	−	1.67771i
$680$	−0.910381	−	0.525609i	−0.0349115	−	0.0201562i
$681$	23.0119	+	14.4606i	0.881817	+	0.554133i
$682$		−	1.91937i		−	0.0734967i
$683$	31.4634	+	18.1654i	1.20391	+	0.695080i	0.961423	−	0.275074i	$-0.0887023\pi$
$683$	31.4634	+	18.1654i	1.20391	+	0.695080i	0.242490	+	0.970154i	$0.422036\pi$
$684$	−0.243112	+	3.24051i	−0.00929560	+	0.123904i
$685$			7.85974i			0.300305i
$686$	4.01733	+	18.0793i	0.153382	+	0.690271i
$687$	−10.2454	+	16.3040i	−0.390887	+	0.622036i
$688$	10.0952			0.384875
$689$	−1.56313	−	2.70741i	−0.0595504	−	0.103144i
$690$	5.15565	−	2.72457i	0.196272	−	0.103723i
$691$	21.5677	+	12.4521i	0.820474	+	0.473701i	0.850580	−	0.525846i	$-0.176251\pi$
$691$	21.5677	+	12.4521i	0.820474	+	0.473701i	−0.0301056	+	0.999547i	$0.509584\pi$
$692$	14.0710			0.534900
$693$	−1.76249	+	4.81246i	−0.0669515	+	0.182810i
$694$	−36.5220			−1.38636
$695$	−19.3599	−	11.1774i	−0.734363	−	0.423985i
$696$	−0.221362	+	5.90950i	−0.00839072	+	0.223999i
$697$	2.28005	+	3.94917i	0.0863632	+	0.149585i
$698$	0.936631			0.0354520
$699$	39.7013	+	1.48716i	1.50164	+	0.0562495i
$700$	−2.54549	−	0.721453i	−0.0962104	−	0.0272684i
$701$		−	35.4297i		−	1.33816i	−0.743190	−	0.669081i	$-0.766688\pi$
$701$		−	35.4297i		−	1.33816i	0.743190	−	0.669081i	$-0.233312\pi$
$702$	1.26848	−	0.553246i	0.0478758	−	0.0208809i
$703$	2.57360	+	1.48587i	0.0970653	+	0.0560407i
$704$			0.645696i			0.0243356i
$705$	−0.0822392	+	0.0434603i	−0.00309731	+	0.00163681i
$706$	7.21594	+	4.16613i	0.271576	+	0.156794i
$707$	−0.851222	+	0.827083i	−0.0320135	+	0.0311056i
$708$	8.73332	−	4.61523i	0.328218	−	0.173451i
$709$	−23.7707	+	41.1721i	−0.892728	+	1.54625i	−0.0561372	+	0.998423i	$0.517878\pi$
$709$	−23.7707	+	41.1721i	−0.892728	+	1.54625i	−0.836591	+	0.547828i	$0.815455\pi$
$710$	−5.37823	+	9.31536i	−0.201841	+	0.349599i
$711$	12.9286	+	0.969939i	0.484861	+	0.0363756i
$712$	−10.6056	+	6.12312i	−0.397460	+	0.229474i
$713$	−5.00387	−	8.66695i	−0.187396	−	0.324580i
$714$	3.57821	−	3.22531i	0.133911	−	0.120704i
$715$	−0.0859835	+	0.148928i	−0.00321560	+	0.00556958i
$716$			13.8635i			0.518105i
$717$	2.08689	+	3.94899i	0.0779364	+	0.147478i
$718$	−23.3109			−0.869956
$719$	6.86251	+	11.8862i	0.255928	+	0.443281i	0.965147	−	0.261707i	$-0.0842855\pi$
$719$	6.86251	+	11.8862i	0.255928	+	0.443281i	−0.709219	+	0.704988i	$0.750952\pi$
$720$	−2.99159	−	0.224437i	−0.111490	−	0.00836429i
$721$	10.4529	+	10.7580i	0.389287	+	0.400649i
$722$	−15.4383	+	8.91333i	−0.574556	+	0.331720i
$723$	19.6000	−	31.1904i	0.728934	−	1.15998i
$724$	−8.51106	+	4.91386i	−0.316311	+	0.182622i
$725$	2.95682	−	1.70712i	0.109814	−	0.0634010i
$726$	8.56456	+	16.2066i	0.317861	+	0.601482i
$727$	38.0093	−	21.9447i	1.40969	−	0.813883i	0.414328	−	0.910127i	$-0.364016\pi$
$727$	38.0093	−	21.9447i	1.40969	−	0.813883i	0.995358	+	0.0962448i	$0.0306832\pi$
$728$	0.172566	+	0.683180i	0.00639574	+	0.0253203i
$729$	−26.3216	−	6.01459i	−0.974873	−	0.222762i
$730$	−8.03384	−	13.9150i	−0.297346	−	0.515018i
$731$	10.6122			0.392507
$732$	−3.26558	+	5.19667i	−0.120699	+	0.192074i
$733$			9.46051i			0.349432i	0.984619	+	0.174716i	$0.0559007\pi$
$733$			9.46051i			0.349432i	−0.984619	+	0.174716i	$0.944099\pi$
$734$	−2.24825	+	3.89409i	−0.0829845	+	0.143733i
$735$	6.74354	−	10.0759i	0.248739	−	0.371657i
$736$	1.68335	+	2.91565i	0.0620491	+	0.107472i
$737$	−4.03762	+	2.33112i	−0.148728	+	0.0858679i
$738$	10.7519	+	7.33181i	0.395782	+	0.269888i
$739$	1.16306	−	2.01449i	0.0427840	−	0.0741041i	−0.843840	−	0.536594i	$-0.819711\pi$
$739$	1.16306	−	2.01449i	0.0427840	−	0.0741041i	0.886624	+	0.462490i	$0.153044\pi$
$740$	−1.37174	+	2.37592i	−0.0504260	+	0.0873404i
$741$	−0.423076	−	0.265861i	−0.0155421	−	0.00976664i
$742$	−29.8798	−	8.46868i	−1.09692	−	0.310895i
$743$	3.14789	+	1.81743i	0.115485	+	0.0666752i	0.556630	−	0.830761i	$-0.312094\pi$
$743$	3.14789	+	1.81743i	0.115485	+	0.0666752i	−0.441145	+	0.897436i	$0.645428\pi$
$744$	−0.192726	+	5.14503i	−0.00706568	+	0.188626i
$745$		−	15.7141i		−	0.575719i
$746$	26.9720	+	15.5723i	0.987515	+	0.570142i
$747$	6.18652	−	9.07235i	0.226353	−	0.331940i
$748$			0.678767i			0.0248182i
$749$	−2.76674	+	9.76181i	−0.101094	+	0.356689i
$750$	0.809270	+	1.53137i	0.0295504	+	0.0559176i
$751$	−13.4034			−0.489097			−0.244548	−	0.969637i	$-0.578640\pi$
$751$	−13.4034			−0.489097			−0.244548	+	0.969637i	$0.578640\pi$
$752$	−0.0268516	−	0.0465083i	−0.000979176	−	0.00169598i
$753$	−29.3982	−	18.4738i	−1.07133	−	0.673223i
$754$	−0.787485	−	0.454655i	−0.0286785	−	0.0165576i
$755$	6.46602			0.235323
$756$	5.20771	−	12.7232i	0.189403	−	0.462738i
$757$	9.85725			0.358268			0.179134	−	0.983825i	$-0.442670\pi$
$757$	9.85725			0.358268			0.179134	+	0.983825i	$0.442670\pi$
$758$	6.08070	+	3.51069i	0.220861	+	0.127514i
$759$	−3.18804	−	2.00336i	−0.115719	−	0.0727174i
$760$	0.541602	+	0.938083i	0.0196460	+	0.0340278i
$761$	39.8245			1.44364			0.721818	−	0.692083i	$-0.243307\pi$
$761$	39.8245			1.44364			0.721818	+	0.692083i	$0.243307\pi$
$762$	5.81412	+	11.0019i	0.210623	+	0.398558i
$763$	10.0007	+	39.5921i	0.362049	+	1.43333i
$764$		−	19.0586i		−	0.689514i
$765$	−3.14482	−	0.235932i	−0.113701	−	0.00853016i
$766$	−13.7902	−	7.96179i	−0.498261	−	0.287671i
$767$			1.51886i			0.0548428i
$768$	0.0648349	−	1.73084i	0.00233953	−	0.0624562i
$769$	−36.9471	−	21.3314i	−1.33235	−	0.769231i	−0.346688	−	0.937981i	$-0.612694\pi$
$769$	−36.9471	−	21.3314i	−1.33235	−	0.769231i	−0.985659	+	0.168750i	$0.946027\pi$
$770$	0.418377	+	1.65633i	0.0150772	+	0.0596900i
$771$	−6.88762	−	4.32818i	−0.248052	−	0.155875i
$772$	−7.28322	+	12.6149i	−0.262129	+	0.454020i
$773$	−5.52090	+	9.56248i	−0.198573	+	0.343939i	−0.948066	−	0.318074i	$-0.896964\pi$
$773$	−5.52090	+	9.56248i	−0.198573	+	0.343939i	0.749493	+	0.662012i	$0.230297\pi$
$774$	27.2874	−	13.1381i	0.980825	−	0.472241i
$775$	2.57432	−	1.48628i	0.0924722	−	0.0533889i
$776$	−8.58718	−	14.8734i	−0.308262	−	0.533925i
$777$	−8.41743	−	9.33843i	−0.301974	−	0.335014i
$778$	−4.47198	+	7.74569i	−0.160328	+	0.277696i
$779$		−	4.69886i		−	0.168354i
$780$	0.245439	−	0.390578i	0.00878813	−	0.0139850i
$781$	6.94540			0.248526
$782$	1.76957	+	3.06498i	0.0632796	+	0.109603i
$783$	7.09245	+	16.2616i	0.253463	+	0.581141i
$784$	5.95901	+	3.67290i	0.212822	+	0.131175i
$785$	−13.1731	+	7.60552i	−0.470170	+	0.271453i
$786$	−0.0605319	−	0.114543i	−0.00215910	−	0.00408563i
$787$	−11.6514	+	6.72696i	−0.415329	+	0.239790i	−0.693077	−	0.720864i	$-0.743745\pi$
$787$	−11.6514	+	6.72696i	−0.415329	+	0.239790i	0.277748	+	0.960654i	$0.410412\pi$
$788$	−15.6904	+	9.05884i	−0.558946	+	0.322708i
$789$	−11.1781	+	17.7882i	−0.397952	+	0.633278i
$790$	3.74266	−	2.16082i	0.133158	−	0.0768787i
$791$	−8.09974	+	2.04593i	−0.287994	+	0.0727451i
$792$	0.840327	+	1.74533i	0.0298597	+	0.0620175i
$793$	−0.471868	−	0.817299i	−0.0167565	−	0.0290231i
$794$	−1.56935			−0.0556942
$795$	9.49949	+	17.9757i	0.336912	+	0.637533i
$796$		−	15.5925i		−	0.552661i
$797$	18.3399	−	31.7656i	0.649631	−	1.12519i	−0.333580	−	0.942722i	$-0.608257\pi$
$797$	18.3399	−	31.7656i	0.649631	−	1.12519i	0.983211	−	0.182472i	$-0.0584100\pi$
$798$	−4.85484	+	1.03465i	−0.171859	+	0.0366263i
$799$	−0.0282268	−	0.0488903i	−0.000998594	−	0.00172962i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−20.6982	+	30.3533i	−0.731334	+	1.07248i
$802$	16.9202	−	29.3066i	0.597472	−	1.03485i
$803$	−5.18742	+	8.98488i	−0.183060	+	0.317069i
$804$	11.0572	−	5.84332i	0.389958	−	0.206078i
$805$	6.20728	+	6.38845i	0.218778	+	0.225163i
$806$	−0.685613	−	0.395839i	−0.0241497	−	0.0139428i
$807$	14.4713	−	7.64755i	0.509414	−	0.269206i
$808$			0.448592i			0.0157814i
$809$	14.9049	+	8.60538i	0.524030	+	0.302549i	0.738582	−	0.674164i	$-0.235496\pi$
$809$	14.9049	+	8.60538i	0.524030	+	0.302549i	−0.214552	+	0.976713i	$0.568829\pi$
$810$	−8.37841	+	3.28669i	−0.294387	+	0.115482i
$811$			5.81435i			0.204169i	0.994776	+	0.102085i	$0.0325513\pi$
$811$			5.81435i			0.204169i	−0.994776	+	0.102085i	$0.967449\pi$
$812$	−8.75817	+	2.21225i	−0.307351	+	0.0776347i
$813$	−1.41796	−	0.0531150i	−0.0497301	−	0.00186282i
$814$	1.77145			0.0620893
$815$	−5.32485	−	9.22290i	−0.186521	−	0.323064i
$816$	0.0681556	−	1.81949i	0.00238592	−	0.0636948i
$817$	−9.47010	−	5.46757i	−0.331317	−	0.191286i
$818$	8.62971			0.301731
$819$	1.35556	+	1.62206i	0.0473671	+	0.0566795i
$820$	4.33793			0.151487
$821$	27.6833	+	15.9830i	0.966154	+	0.557810i	0.898062	−	0.439869i	$-0.144975\pi$
$821$	27.6833	+	15.9830i	0.966154	+	0.557810i	0.0680927	+	0.997679i	$0.478309\pi$
$822$	−12.0361	+	6.36065i	−0.419808	+	0.221853i
$823$	−12.8380	−	22.2360i	−0.447504	−	0.775100i	0.550719	−	0.834691i	$-0.314354\pi$
$823$	−12.8380	−	22.2360i	−0.447504	−	0.775100i	−0.998223	+	0.0595911i	$0.981020\pi$
$824$	5.66944			0.197504
$825$	0.595052	−	0.946934i	0.0207171	−	0.0329680i
$826$	10.5147	+	10.8216i	0.365854	+	0.376532i
$827$		−	38.7042i		−	1.34588i	−0.739698	−	0.672939i	$-0.765032\pi$
$827$		−	38.7042i		−	1.34588i	0.739698	−	0.672939i	$-0.234968\pi$
$828$	8.34462	+	5.69028i	0.289996	+	0.197751i
$829$	9.07060	+	5.23691i	0.315035	+	0.181885i	0.649177	−	0.760637i	$-0.275113\pi$
$829$	9.07060	+	5.23691i	0.315035	+	0.181885i	−0.334142	+	0.942523i	$0.608447\pi$
$830$		−	3.66030i		−	0.127051i
$831$	3.54921	+	2.23032i	0.123121	+	0.0773689i
$832$	0.230647	+	0.133164i	0.00799624	+	0.00461663i
$833$	6.26422	+	3.86102i	0.217042	+	0.133776i
$834$	1.44938	−	38.6927i	0.0501878	−	1.33982i
$835$	−9.89716	+	17.1424i	−0.342505	+	0.593237i
$836$	0.349710	−	0.605716i	0.0120950	−	0.0209491i
$837$	6.17494	+	14.1579i	0.213437	+	0.489369i
$838$	−11.7415	+	6.77897i	−0.405604	+	0.234176i
$839$	18.1028	+	31.3549i	0.624977	+	1.08249i	0.988545	+	0.150925i	$0.0482251\pi$
$839$	18.1028	+	31.3549i	0.624977	+	1.08249i	−0.363568	+	0.931568i	$0.618442\pi$
$840$	−0.955176	−	4.48192i	−0.0329567	−	0.154641i
$841$	−8.67146	+	15.0194i	−0.299016	+	0.517911i
$842$		−	3.29962i		−	0.113713i
$843$	−8.92235	−	0.334220i	−0.307302	−	0.0115111i
$844$	−3.31189			−0.114000
$845$	−6.46453	−	11.1969i	−0.222387	−	0.385185i
$846$	−0.133107	−	0.0907672i	−0.00457633	−	0.00312064i
$847$	−20.0818	+	19.5123i	−0.690019	+	0.670452i
$848$	−10.1657	+	5.86918i	−0.349092	+	0.201548i
$849$	−32.1858	−	1.20564i	−1.10461	−	0.0413774i
$850$	−0.910381	+	0.525609i	−0.0312258	+	0.0180282i
$851$	7.99899	−	4.61822i	0.274202	−	0.158311i
$852$	−18.6177	−	0.697394i	−0.637831	−	0.0238923i
$853$	−36.2033	+	20.9020i	−1.23958	+	0.715671i	−0.969008	−	0.247030i	$-0.920545\pi$
$853$	−36.2033	+	20.9020i	−1.23958	+	0.715671i	−0.270570	+	0.962700i	$0.587212\pi$
$854$	−9.01996	−	2.55648i	−0.308657	−	0.0874808i
$855$	2.68481	+	1.83079i	0.0918184	+	0.0626118i
$856$	1.91747	+	3.32116i	0.0655379	+	0.113515i
$857$	14.3813			0.491256			0.245628	−	0.969364i	$-0.421006\pi$
$857$	14.3813			0.491256			0.245628	+	0.969364i	$0.421006\pi$
$858$	−0.297647	−	0.0111495i	−0.0101615	−	0.000380637i
$859$			16.2444i			0.554252i	0.960834	+	0.277126i	$0.0893819\pi$
$859$			16.2444i			0.554252i	−0.960834	+	0.277126i	$0.910618\pi$
$860$	5.04758	−	8.74267i	0.172121	−	0.298123i
$861$	−6.13277	+	18.9092i	−0.209004	+	0.644425i
$862$	−9.85901	−	17.0763i	−0.335799	−	0.581621i
$863$	−1.73844	+	1.00369i	−0.0591773	+	0.0341660i	−0.529297	−	0.848437i	$-0.677544\pi$
$863$	−1.73844	+	1.00369i	−0.0591773	+	0.0341660i	0.470119	+	0.882603i	$0.344211\pi$
$864$	−2.07731	−	4.76285i	−0.0706715	−	0.162036i
$865$	7.03552	−	12.1859i	0.239215	−	0.414332i
$866$	−2.27257	+	3.93621i	−0.0772251	+	0.133758i
$867$	−1.03055	+	27.5116i	−0.0349992	+	0.934341i
$868$	−7.62518	+	1.92606i	−0.258815	+	0.0653749i
$869$	−2.41662	−	1.39524i	−0.0819782	−	0.0473301i
$870$	5.00710	+	3.14646i	0.169757	+	0.106675i
$871$			1.92302i			0.0651590i
$872$	13.3666	+	7.71722i	0.452651	+	0.261338i
$873$	−42.5680	−	29.0275i	−1.44071	−	0.982432i
$874$		−	3.64682i		−	0.123356i
$875$	−1.89754	+	1.84373i	−0.0641486	+	0.0623294i
$876$	14.8074	−	23.5638i	0.500297	−	0.796146i
$877$	−47.1351			−1.59164			−0.795819	−	0.605534i	$-0.792959\pi$
$877$	−47.1351			−1.59164			−0.795819	+	0.605534i	$0.792959\pi$
$878$	8.66968	+	15.0163i	0.292588	+	0.506777i
$879$	−41.4433	+	21.9012i	−1.39785	+	0.738710i
$880$	0.559189	+	0.322848i	0.0188503	+	0.0108832i
$881$	45.7938			1.54283			0.771416	−	0.636331i	$-0.219549\pi$
$881$	45.7938			1.54283			0.771416	+	0.636331i	$0.219549\pi$
$882$	20.8873	+	2.17268i	0.703312	+	0.0731580i
$883$	50.8663			1.71179			0.855894	−	0.517151i	$-0.173007\pi$
$883$	50.8663			1.71179			0.855894	+	0.517151i	$0.173007\pi$
$884$	0.242460	+	0.139984i	0.00815481	+	0.00470818i
$885$	0.369751	−	9.87090i	0.0124290	−	0.331807i
$886$	−0.491301	−	0.850958i	−0.0165056	−	0.0285885i
$887$	14.3175			0.480733			0.240367	−	0.970682i	$-0.422732\pi$
$887$	14.3175			0.480733			0.240367	+	0.970682i	$0.422732\pi$
$888$	−4.74850	−	0.177873i	−0.159349	−	0.00596902i
$889$	−13.6327	+	13.2461i	−0.457226	+	0.444260i
$890$			12.2462i			0.410495i
$891$	4.54283	+	3.62402i	0.152191	+	0.121409i
$892$	−17.3057	−	9.99144i	−0.579437	−	0.334538i
$893$			0.0581715i			0.00194663i
$894$	24.0640	−	12.7169i	0.804820	−	0.425317i
$895$	12.0062	+	6.93177i	0.401322	+	0.231703i
$896$	2.56518	−	0.647947i	0.0856968	−	0.0216464i
$897$	−1.37309	+	0.725629i	−0.0458463	+	0.0242280i
$898$	−14.8221	+	25.6726i	−0.494619	+	0.856704i
$899$	5.07454	−	8.78936i	0.169245	−	0.293141i
$900$	−1.69016	+	2.47858i	−0.0563388	+	0.0826192i
$901$	−10.6864	+	6.16978i	−0.356015	+	0.205545i
$902$	−1.40049	−	2.42572i	−0.0466313	−	0.0807678i
$903$	30.9737	+	34.3627i	1.03074	+	1.14352i
$904$	−1.57878	+	2.73453i	−0.0525096	+	0.0909492i
$905$			9.82773i			0.326685i
$906$	5.23276	+	9.90185i	0.173847	+	0.328967i
$907$	24.5154			0.814019			0.407010	−	0.913424i	$-0.366572\pi$
$907$	24.5154			0.814019			0.407010	+	0.913424i	$0.366572\pi$
$908$	7.84568	+	13.5891i	0.260368	+	0.450971i
$909$	0.583810	+	1.21255i	0.0193638	+	0.0402178i
$910$	0.677935	+	0.192143i	0.0224733	+	0.00636949i
$911$	−24.2755	+	14.0155i	−0.804283	+	0.464353i	−0.844967	−	0.534819i	$-0.820380\pi$
$911$	−24.2755	+	14.0155i	−0.804283	+	0.464353i	0.0406837	+	0.999172i	$0.487046\pi$
$912$	−0.998246	+	1.58855i	−0.0330552	+	0.0526023i
$913$	−2.04680	+	1.18172i	−0.0677393	+	0.0391093i
$914$	10.1352	−	5.85157i	0.335243	−	0.193553i
$915$	2.86765	+	5.42641i	0.0948017	+	0.179392i
$916$	−9.62794	+	5.55869i	−0.318116	+	0.183664i
$917$	0.141933	−	0.137908i	0.00468703	−	0.00455411i
$918$	−2.18370	−	5.00680i	−0.0720730	−	0.165249i
$919$	4.86440	+	8.42539i	0.160462	+	0.277928i	0.935034	−	0.354557i	$-0.115368\pi$
$919$	4.86440	+	8.42539i	0.160462	+	0.277928i	−0.774573	+	0.632485i	$0.782035\pi$
$920$	3.36670			0.110997
$921$	−24.4693	+	38.9391i	−0.806292	+	1.28309i
$922$		−	36.5185i		−	1.20267i
$923$	1.43237	−	2.48094i	0.0471471	−	0.0816612i
$924$	−2.19787	+	1.98110i	−0.0723045	+	0.0651736i
$925$	1.37174	+	2.37592i	0.0451024	+	0.0781196i
$926$	−1.88543	+	1.08855i	−0.0619590	+	0.0357721i
$927$	15.3246	−	7.37837i	0.503325	−	0.242337i
$928$	−1.70712	+	2.95682i	−0.0560391	+	0.0970625i
$929$	3.74795	−	6.49163i	0.122966	−	0.212984i	−0.797970	−	0.602697i	$-0.794093\pi$
$929$	3.74795	−	6.49163i	0.122966	−	0.212984i	0.920936	+	0.389714i	$0.127426\pi$
$930$	4.35936	+	2.73942i	0.142949	+	0.0898291i
$931$	−3.60079	−	6.67290i	−0.118011	−	0.218695i
$932$	19.8646	+	11.4688i	0.650686	+	0.375674i
$933$	−0.931624	+	24.8707i	−0.0305000	+	0.814230i
$934$		−	24.5562i		−	0.803505i
$935$	0.587830	+	0.339384i	0.0192241	+	0.0110990i
$936$	0.796745	+	0.0597740i	0.0260424	+	0.00195377i
$937$			46.3019i			1.51262i	0.654216	+	0.756308i	$0.272999\pi$
$937$			46.3019i			1.51262i	−0.654216	+	0.756308i	$0.727001\pi$
$938$	13.3126	+	13.7012i	0.434673	+	0.447359i
$939$	−8.87805	−	16.7998i	−0.289724	−	0.548240i
$940$	−0.0537031			−0.00175160
$941$	22.1367	+	38.3419i	0.721637	+	1.24991i	0.960343	+	0.278820i	$0.0899433\pi$
$941$	22.1367	+	38.3419i	0.721637	+	1.24991i	−0.238706	+	0.971092i	$0.576723\pi$
$942$	−22.3075	−	14.0180i	−0.726816	−	0.456731i
$943$	−12.6479	−	7.30225i	−0.411871	−	0.237794i
$944$	5.70296			0.185616
$945$	−8.41476	−	10.8716i	−0.273732	−	0.353653i
$946$	−6.51841			−0.211932
$947$	44.0948	+	25.4582i	1.43289	+	0.827279i	0.997340	−	0.0728856i	$-0.0232208\pi$
$947$	44.0948	+	25.4582i	1.43289	+	0.827279i	0.435549	+	0.900165i	$0.356554\pi$
$948$	6.33783	+	3.98269i	0.205843	+	0.129352i
$949$	2.13964	+	3.70596i	0.0694556	+	0.120301i
$950$	1.08320			0.0351438
$951$	13.4984	+	25.5428i	0.437716	+	0.828282i
$952$	2.69657	−	0.681133i	0.0873962	−	0.0220756i
$953$			21.9222i			0.710131i	0.934841	+	0.355066i	$0.115541\pi$
$953$			21.9222i			0.710131i	−0.934841	+	0.355066i	$0.884459\pi$
$954$	−19.8398	+	29.0944i	−0.642336	+	0.941966i
$955$	−16.5052	−	9.52928i	−0.534095	−	0.308360i
$956$			2.57874i			0.0834023i
$957$	0.142933	−	3.81574i	0.00462036	−	0.123346i
$958$	26.0736	+	15.0536i	0.842399	+	0.486359i
$959$	−14.4912	−	14.9142i	−0.467946	−	0.481604i
$960$	−1.46653	−	0.921567i	−0.0473321	−	0.0297435i
$961$	−11.0819	+	19.1945i	−0.357481	+	0.619176i
$962$	0.365332	−	0.632773i	0.0117788	−	0.0204014i
$963$	9.50521	+	6.48169i	0.306301	+	0.208870i
$964$	18.4188	−	10.6341i	0.593229	−	0.342501i
$965$	7.28322	+	12.6149i	0.234455	+	0.406088i
$966$	−4.75969	+	14.6756i	−0.153140	+	0.472180i
$967$	26.5952	−	46.0643i	0.855245	−	1.48133i	−0.0211717	−	0.999776i	$-0.506740\pi$
$967$	26.5952	−	46.0643i	0.855245	−	1.48133i	0.876417	−	0.481553i	$-0.159927\pi$
$968$			10.5831i			0.340153i
$969$	−1.04937	+	1.66992i	−0.0337107	+	0.0536454i
$970$	−17.1744			−0.551435
$971$	−11.2333	−	19.4567i	−0.360494	−	0.624394i	0.627548	−	0.778578i	$-0.284059\pi$
$971$	−11.2333	−	19.4567i	−0.360494	−	0.624394i	−0.988042	+	0.154184i	$0.950725\pi$
$972$	−11.8135	−	10.1706i	−0.378919	−	0.326222i
$973$	57.3444	−	14.4848i	1.83838	−	0.464360i
$974$	19.6750	−	11.3594i	0.630428	−	0.363978i
$975$	−0.215531	−	0.407846i	−0.00690252	−	0.0130615i
$976$	−3.06877	+	1.77175i	−0.0982289	+	0.0567125i
$977$	−38.3951	+	22.1674i	−1.22837	+	0.709199i	−0.966688	−	0.255956i	$-0.917610\pi$
$977$	−38.3951	+	22.1674i	−1.22837	+	0.709199i	−0.261680	+	0.965155i	$0.584276\pi$
$978$	9.81441	−	15.6181i	0.313830	−	0.499412i
$979$	6.84797	−	3.95368i	0.218862	−	0.126360i
$980$	6.16033	−	3.32420i	0.196785	−	0.106188i
$981$	46.1735	+	3.46406i	1.47421	+	0.110599i
$982$	−9.15511	−	15.8571i	−0.292151	−	0.506021i
$983$	−2.36362			−0.0753878			−0.0376939	−	0.999289i	$-0.512001\pi$
$983$	−2.36362			−0.0753878			−0.0376939	+	0.999289i	$0.512001\pi$
$984$	3.51055	+	6.64296i	0.111912	+	0.211770i
$985$			18.1177i			0.577277i
$986$	−1.79456	+	3.10827i	−0.0571504	+	0.0989874i
$987$	0.0759231	−	0.234095i	0.00241666	−	0.00745131i
$988$	−0.144244	−	0.249838i	−0.00458901	−	0.00794840i
$989$	−29.4339	+	16.9937i	−0.935945	+	0.540368i
$990$	1.93166	+	0.144918i	0.0613922	+	0.00460581i
$991$	−6.59191	+	11.4175i	−0.209399	+	0.362690i	−0.951525	−	0.307570i	$-0.900484\pi$
$991$	−6.59191	+	11.4175i	−0.209399	+	0.362690i	0.742126	+	0.670260i	$0.233817\pi$
$992$	−1.48628	+	2.57432i	−0.0471895	+	0.0817347i
$993$	8.49604	−	4.48984i	0.269614	−	0.142481i
$994$	−6.96961	−	27.5923i	−0.221063	−	0.875174i
$995$	−13.5035	−	7.79625i	−0.428090	−	0.247158i
$996$	5.60527	−	2.96217i	0.177610	−	0.0938601i
$997$			35.4910i			1.12401i	0.827134	+	0.562005i	$0.189970\pi$
$997$			35.4910i			1.12401i	−0.827134	+	0.562005i	$0.810030\pi$
$998$	−19.7793	−	11.4196i	−0.626101	−	0.361480i
$999$	−13.0668	+	5.69904i	−0.413414	+	0.180310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.15	✓	32
3.2	odd	2		1890.2.t.c.1151.4		32
7.5	odd	6		630.2.bk.c.131.8	yes	32
9.2	odd	6		630.2.bk.c.101.16	yes	32
9.7	even	3		1890.2.bk.c.521.9		32
21.5	even	6		1890.2.bk.c.341.9		32
63.47	even	6	inner	630.2.t.c.551.15	yes	32
63.61	odd	6		1890.2.t.c.1601.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.15	✓	32	1.1	even	1	trivial
630.2.t.c.551.15	yes	32	63.47	even	6	inner
630.2.bk.c.101.16	yes	32	9.2	odd	6
630.2.bk.c.131.8	yes	32	7.5	odd	6
1890.2.t.c.1151.4		32	3.2	odd	2
1890.2.t.c.1601.4		32	63.61	odd	6
1890.2.bk.c.341.9		32	21.5	even	6
1890.2.bk.c.521.9		32	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.46653 + 0.921567i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.809270 + 1.53137i) q^{6} +(-1.89754 + 1.84373i) q^{7} +1.00000i q^{8} +(1.30143 + 2.70301i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.46653 + 0.921567i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.809270 + 1.53137i) q^{6} +(-1.89754 + 1.84373i) q^{7} +1.00000i q^{8} +(1.30143 + 2.70301i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.645696i q^{11} +(-0.0648349 + 1.73084i) q^{12} +(-0.230647 - 0.133164i) q^{13} +(-2.56518 + 0.647947i) q^{14} +(1.46653 + 0.921567i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.525609 + 0.910381i) q^{17} +(-0.224437 + 2.99159i) q^{18} +(0.938083 - 0.541602i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.48192 + 0.955176i) q^{21} +(0.322848 - 0.559189i) q^{22} -3.36670i q^{23} +(-0.921567 + 1.46653i) q^{24} +1.00000 q^{25} +(-0.133164 - 0.230647i) q^{26} +(-0.582424 + 5.16341i) q^{27} +(-2.54549 - 0.721453i) q^{28} +(2.95682 - 1.70712i) q^{29} +(0.809270 + 1.53137i) q^{30} +(2.57432 - 1.48628i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.595052 - 0.946934i) q^{33} +(-0.910381 + 0.525609i) q^{34} +(-1.89754 + 1.84373i) q^{35} +(-1.69016 + 2.47858i) q^{36} +(1.37174 + 2.37592i) q^{37} +1.08320 q^{38} +(-0.215531 - 0.407846i) q^{39} +1.00000i q^{40} +(2.16896 - 3.75676i) q^{41} +(-4.35905 - 1.41375i) q^{42} +(-5.04758 - 8.74267i) q^{43} +(0.559189 - 0.322848i) q^{44} +(1.30143 + 2.70301i) q^{45} +(1.68335 - 2.91565i) q^{46} +(-0.0268516 + 0.0465083i) q^{47} +(-1.53137 + 0.809270i) q^{48} +(0.201321 - 6.99710i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-1.60980 + 0.850719i) q^{51} -0.266328i q^{52} +(10.1657 + 5.86918i) q^{53} +(-3.08610 + 4.18043i) q^{54} -0.645696i q^{55} +(-1.84373 - 1.89754i) q^{56} +(1.87485 + 0.0702295i) q^{57} +3.41425 q^{58} +(-2.85148 - 4.93891i) q^{59} +(-0.0648349 + 1.73084i) q^{60} +(3.06877 + 1.77175i) q^{61} +2.97257 q^{62} +(-7.45314 - 2.72960i) q^{63} -1.00000 q^{64} +(-0.230647 - 0.133164i) q^{65} +(0.988797 - 0.522542i) q^{66} +(-3.61024 - 6.25312i) q^{67} -1.05122 q^{68} +(3.10264 - 4.93737i) q^{69} +(-2.56518 + 0.647947i) q^{70} +10.7565i q^{71} +(-2.70301 + 1.30143i) q^{72} +(-13.9150 - 8.03384i) q^{73} +2.74347i q^{74} +(1.46653 + 0.921567i) q^{75} +(0.938083 + 0.541602i) q^{76} +(1.19049 + 1.22523i) q^{77} +(0.0172674 - 0.460970i) q^{78} +(2.16082 - 3.74266i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-5.61257 + 7.03556i) q^{81} +(3.75676 - 2.16896i) q^{82} +(-1.83015 - 3.16992i) q^{83} +(-3.06817 - 3.40387i) q^{84} +(-0.525609 + 0.910381i) q^{85} -10.0952i q^{86} +(5.90950 + 0.221362i) q^{87} +0.645696 q^{88} +(6.12312 + 10.6056i) q^{89} +(-0.224437 + 2.99159i) q^{90} +(0.683180 - 0.172566i) q^{91} +(2.91565 - 1.68335i) q^{92} +(5.14503 + 0.192726i) q^{93} +(-0.0465083 + 0.0268516i) q^{94} +(0.938083 - 0.541602i) q^{95} +(-1.73084 - 0.0648349i) q^{96} +(-14.8734 + 8.58718i) q^{97} +(3.67290 - 5.95901i) q^{98} +(1.74533 - 0.840327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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